F (x) = 6x^2 + 6x + 12 (Solve by factoring.)

You can't solve for the zeros by factoring because the function is not factorable.

I'll show you what happens:

f (x) = 6x^2 + 6x + 12

To solve for the zeros (when f (x) = 0), set f (x) equal to 0.

0 = 6x^2 + 6x + 12

First you can factor out a 6.

0 = 6 (x^2 + x + 2)

Divide by 6.

0 = x^2 + x + 2

Now you need two integers that add up to the coefficient of x (1) and multiply to the product of the last term and the coefficient of x^2. This number is 2.

No two integers add up to 1 and multiply to 2.