As the heading recommend here we will be solving quadratic equations by factoring them.
Zero factor property or zero factor principle
To solving quadric equation by factor we will required the following fact.
If ab = 0 then either a= 0 and/or b = 0
This fact is the zero factor principle or zero factor property. All the fact says that if two term product is zero then at least one of the terms had to be zero to begin with.
Notice that it fact will only work if the product is equal to zero. Assume the following product.
ab = 6
In this case there is no cause to believe that either a or b will be 6. We could have a = 2 and
b =3 for example. Thus, do not misuse this fact!
In order to solve a quadratic equation by factoring first we have to move all the terms over to one side of the equation. Doing this serves two causes. First, this puts the quadratics into a form which can be factored. Secondly, and possibly more importantly, to use the zero factor property we have to have a zero on one side of the equation. If we don't have a zero on one side of the equation we can't use the zero factor property.