I already know the answer from the solutions manual. It says it's A+C.
However, I don't see how it's A+C. I don't even know what I'm doing anymore. I've tried applying De Morgan's law to (A'+B') but that leads me nowhere. I've tried using the both distributive laws and it's just complicated things more. I'm probably missing something huge. Any pointers to how it's A+C?

 

First thing you might consider is seeing if you agree with the claimed solution. Doing so will probably give you some insight into how the terms interact.

So see if you agree that if A is True, that the whole thing is True regardless of what B and C are.

Then do the same for C.

The see if you agree that, if A and C are both False, that the whole thing is False no matter what B is.

Another step you might take is to draw a Truth Table for the original expression.

If you know how to use Karnaugh maps, that can also give you visibility into how things can be rearranged to get at what you want.

 

I drew a quick Karnaugh Map