SOLUTION: why is it a good idea to factor a quadratic equation before you solve?

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Question 476468: why is it a good idea to factor a quadratic equation before you solve?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

because it's easier!
A quadratic equation has an x%5E2 term and, typically, an x term and a constant. Most people can not see the answer on inspection. If you factor, you can get something like
%28ax%2Bb%29%28cx%2Bd%29+=+0
which makes it very+easy to solve for x.
Why? Since the two expressions, when multiplied, equal 0, that means that one or both of the expressions must be 0, so you can separate them out into two equations:
ax%2Bb=0 and cx%2Bd=0
at which point it is very easy to solve for the two possible values of x.
if ax%2Bb=0 ...->...x=-b%2Fa...one solution
if cx%2Bd=0 ...->...x=-d%2Fc...another solution