Who might stick around?

Clearly, Mr. Musk needs to get as many of Tesla’s biggest shareholders as possible to exchange their public shares for private ones.

But not all of these investors might be able to own substantial stakes in a private company. Some big institutional investors hold Tesla shares in index funds, and would most likely sell in the event of a deal. And in recent months, two of Tesla’s largest holders, T. Rowe Price and Fidelity Management, sold large chunks of their shares in the company.

Here's where Tesla’s broad investor base may help Mr. Musk: Even if some of the top shareholders don't stick around, allowing many of the smaller shareholders to buy in could, in theory, replace the loss of one or two big investors.

Where would the new money come from?

That’s the $24 billion question. Mr. Musk suggested that financing was secured for the deal when he sent his Twitter message on Aug. 7. In his blog post, Mr. Musk elaborated, saying that he had been discussing taking Tesla private with the Saudis for nearly two years.

After a meeting with the managing director of the Saudi fund on July 31, Mr. Musk left with the impression that completing such a deal “was just a matter of getting the process moving,” he said in the blog post. “This is why I referred to ‘funding secured.’” If only it were so simple. The Saudi fund has been mum, and is reportedly considering investing in an upstart electric car company, Lucid Motors, which could complicate a deal with Tesla.

Mr. Musk said he was working with Silver Lake, the private equity firm. Silver Lake took part in the buyout of Dell, and could contribute capital to a deal for Tesla. Institutional investors like T. Rowe Price and Fidelity sometimes take equity stakes in private technology companies, and could do something similar here. And Mr. Musk, a billionaire, could draw on his broad network of relationships and companies, including SpaceX.