BA = CA + C
solve the equation for B, stating any assumption required.
not a clue where to start. Missed that lecture!
If you're allowed to make the assumption that A is invertible, then just multiply both sides of the given equation on the right by the inverse of A, to get $\displaystyle B = C + CA^{-1}$. Otherwise, the problem is a whole lot harder, and the solution, if it exists, will not be unique.