To solve this algebraically, you can first factor out a 3:

Then, you can factor (I'm using guess and check) and my answer is -4 and 2:

From here on, finding 0s is very easy. You just solve for x in the parentheses. So,
the 0s are when x = 4, and x = -2. Remember, (4-4) = 0, and (-2+2) = 0, that's what you want.