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(x^2 + 5x + 6) = 0. Then factor the inside: 2(x + 2)(x + 3) = 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.