Bigger Fronts

A leading coefficient does not change the method. To solve $2x^{2}+10x+12 = 0$, factor out the greatest common factor 2 first: $2\left(x^{2}+5x+6\right) = 0$. Then factor the inside: $2\left(x+2\right)\left(x+3\right) = 0$. Now set each factor equal to zero. The factor 2 can never be zero, so it gives no case. The solutions are $x = -2$ or $x = -3$.

A number factor that is not zero gives no case. Only a factor that contains $x$ can be zero, so only those factors give cases. The equation has two solutions, the same as if the 2 were not there.

You can also divide both sides by 2 at the start, because 2 is not zero. Dividing by an expression that contains the unknown is different. You would first have to check whether it can be zero, or you may lose a solution. Factoring out 2 and dividing both sides by 2 give the same solutions here.