Politically turbulent North Carolina, where Barack Obama won in 2008 and then Republicans rose up to engineer a conservative revolution, has suddenly emerged as a focal point in the presidential race.

The battle lines will be clear Tuesday in dueling rallies in the state’s two major cities.

Presumptive Democratic presidential nominee Hillary Clinton will appear in Charlotte alongside President Obama, who is making his debut on the campaign trail and will try to reenergize his multi­ethnic coalition.

That night, presumptive GOP presidential nominee Donald Trump will take the stage in Raleigh, where he is expected to lambaste Clinton and present her as seeking a third Obama term.

The two campaigns are angling to motivate their core supporters but also to sway a large pool of newly transplanted centrist voters such as Eric and Tonya Mills, both 46, who met here in college and moved back in 2013.

“There’s just something that seems shady to me” about Clinton, Eric Mills, a patent lawyer, said as the couple strode through a “First Friday” street party last week in Raleigh. Still, he said, he did not think he could bring himself to vote for Trump, whose political rise has been a curiosity among those Mills has met on recent business trips overseas. Tonya Mills, a civil engineer, called her vote a “toss-up,” saying that if she had to vote today, she would opt for Clinton, “but it wouldn’t be with my heart behind it.”

North Carolina, with 15 electoral-college votes, is one of a handful of potentially decisive states that both parties see as winnable this year. While Trump has courted working-class whites in old industrial states such as Pennsylvania and Ohio to try to win back places that twice went for Obama, Clinton is seeking to benefit from shifting political winds in North Carolina to help her take back a state that went for Republican Mitt Romney in 2012 and has historically been favorable turf for the GOP.

Clinton’s campaign is banking on a backlash against the controversial law that limits LGBT protections, known as House Bill 2, and longer-term trends working in favor of Democrats: an ongoing influx of college-educated professionals along the urban and suburban corridor that stretches from here to Charlotte, and an uptick in the African American share of the electorate that is part of the legacy of Obama’s elections.

Both of those demographics favor Clinton, while Trump appears strongest in the more rural areas of the state, where tobacco, textiles and furniture-making once defined its character but have since declined in the wake of the free-trade agreements that Trump has criticized.

Tuesday’s rally in Charlotte will be Clinton’s second high-profile event in the state in as many weeks — she previously gave an economic speech here, in the capital — and the campaign is making the kind of investment in staff and television advertising afforded to only seven other battleground states. The campaign says it also will have opened six offices across North Carolina within two weeks.

Trump’s Tuesday rally here comes three weeks after an appearance in Greensboro. But he has only a skeletal staff presence and has yet to take to the airwaves, much to the bewilderment of some fellow Republicans.

“He’s got some real problems to deal with, and I don’t know that I have solutions,” said Carter Wrenn, a longtime GOP strategist who once helped run the political operation of Sen. Jesse Helms (R-N.C.), who died in 2008.

Wrenn said Clinton is smart to be targeting a state where Republicans still have doubts about Trump and where suburban independents are trending toward Clinton.

Dallas Woodhouse, executive director of the state Republican Party, acknowledged that North Carolina is likely to be “a competitive, two-party state for the foreseeable future.” But he argued that Trump should have the upper hand.

For one thing, Woodhouse said, Clinton is not as popular in North Carolina as Obama was, and Obama lost in 2012 even though Charlotte was the site of the Democratic National Convention.

In a statement, Trump predicted he would “do great” in North Carolina.

“People of North Carolina want strength, protection and jobs, and President Obama and Hillary Clinton have let them down for many years,” Trump said. “I will bring jobs back to North Carolina, and our country, like never seen before.”

There has been limited independent polling in the state, but what’s available suggests a competitive contest. One survey released last week by the conservative Civitas Institute put Clinton at 42 percent and Trump at 40 percent, with Libertarian Gary Johnson at 6 percent.

A poll last week by the Democratic firm Greenberg Quinlan Rosner Research found a wider margin, with Clinton leading Trump, 48 percent to 38 percent, and Johnson at 8 percent.

“The Clinton campaign is clearly looking to expand the map,” said Scott Falmlen, a former executive director of the North Carolina Democratic Party.

And it should, he added. “We’re a purple state. With the influx of the new population and the growing urbanization, it’s becoming more Democratic,” he said.

Part of Obama’s aim in North Carolina, aides say, will be to bolster Clinton’s standing among ­college-educated voters and African Americans, as well as among younger voters, who were part of his winning coalition but sided in large numbers during the primaries with Clinton’s rival, Sen. Bernie Sanders of Vermont.

There was a notable lack of enthusiasm for either candidate last week as hundreds of people gathered for the monthly First Friday celebration, where musicians played on the streets and restaurant patrons spilled onto the sidewalks.

Sydney Sumner, 51, arrived in the area nearly a decade ago from California. A single mother, she said she was worried about Latino gang violence.

“Coming from California, I really believed in a secure border,” she said.

On that count, she credits Trump with touching on an important issue — although Sumner said she does not think his solutions are realistic. And she has other issues with Trump.

“You can’t have temper tantrums and be a world leader,” said Sumner, who works in accounting for an automotive after-market parts business.

Sumner grew up as a Republican and was registered as one until Friday night, when she switched to independent.

At First Friday, there were several people milling about with clipboards full of voter-registration forms — many of them at the direction of the Clinton campaign.

“There’s a lot of young people here,” said Joan Cater, 77, a retired nurse and one of those working with the campaign. “They’re transient, and they move. They don’t realize that they have to re-register to vote.”

Voter registration is a key part of Clinton’s strategy in North Carolina, particularly because of the goal of courting new arrivals, including professionals working in banking, biomedicine, technology and other fields.

The number of college-educated adults age 25 and older in North Carolina’s metropolitan regions increased by nearly 656,000 between 2000 and 2014, according to the Carolina Population Center at the University of North Carolina at Chapel Hill. That accounted for more than half of the adult-population growth in those regions during the period.

To win in North Carolina, Clinton will also probably need an Obama-like turnout from African American voters — a group that views Trump highly unfavorably.

According to exit polls, African Americans accounted for about 18 percent of the electorate in 1996. By 2012, the black share of the vote rose to 23 percent.

That was partly because of population growth. But an aggressive effort by the Obama campaign to register new voters and make sure they turned out was also a big factor.

“It was a testament to the effectiveness of the Obama machine,” said Brad Crone, a Raleigh-based Democratic consultant. Whether Clinton can replicate that is “a big question mark,” he said.

Another wild card is whether a backlash against the GOP-produced HB2 will make North Carolina voters more inclined to vote for Democrats.

The law drew national attention earlier this year for forcing people to use only the bathroom that matches the gender on their birth certificate. It also drew fire for blocking local gay rights protections.

In response, businesses have canceled plans to open new offices in the state, conventions have been lost, and entertainers have canceled shows.

The controversy was still fresh last week. Under threat of losing the National Basketball Association All-Star Game in Charlotte next year, the North Carolina legislature considered changes to the law, but on Friday wound up only amending a provision related to bringing anti-discrimination lawsuits — a move that the NBA said did not go far enough.

Clinton has spoken out against HB2. Trump initially said it was unnecessary. He later clarified his position, saying this was a matter for states to decide.

Whether the issue moves votes in the presidential race remains to be seen.

Dave Phillips, an online-marketing manager who moved to Raleigh five years ago, said he considers the law “a joke,” but he said it does not rate high in his deliberations in a presidential race in which “neither of the two candidates seem like great choices.”

Phillips, 33, a registered independent, said he is leaning toward Clinton, in part because Trump, in his view, “is just a sleazeball.”

Juliet Eilperin in Washington contributed to this report.