Bigger Fronts

A leading coefficient does not stop the method. 2x^2 + 10x + 12 = 0: pull the GCF 2 first, 2(x^2 + 5x + 6) = 0, factor the inside, 2(x + 2)(x + 3) = 0, and split. The 2 is a factor that can never be zero, so it contributes no case: x = -2 or x = -3.

A nonzero number factor is a bystander at the split. Only factors that CONTAIN x can vanish, so only they make cases. Two solutions, exactly as if the 2 had never been there.

You could also divide both sides by 2 at the start; dividing by a NUMBER is safe, it is only the unknown you must never divide by. Both routes land on the same pair of answers, as legal routes always do.