It’s the multibillion dollar conundrum facing private equity firms trying to snap up Toshiba Corp.: What to do about the troubled conglomerate’s sensitive nuclear power business?

Toshiba, which had originally opposed a buyout, now plans to solicit proposals from potential investors in a drastic change in stance. The nuclear unit, which is deemed important to Japan’s national security, could be the biggest obstacle to any deal.

As PE giants including Bain Capital, CVC Capital Partners and KKR & Co. consider bids for the company, one of their biggest challenges will be devising a plan that wins government approval. According to experts, they have no easy choices.