Finally, I get it.

Someone posted a method of factoring a while back and I got to asking
myself, why is it that you can factor a trinomial like x^2+5x+6 =0 for
example, come up with two binomials each containing an x, make EACH =
0, and come up with a solution set for x. The factors are (x+2) and (x
+3), so each or both must equal zero.. because of the ZERO PRODUCT
THEOREM which states that if you have 2 real numbers such as a and b,
and you multiply them together and get 0, then one or both of the
numbers must 0. This applies to the (x+2) and (x+3), and since the 3
and the 2 are not 0, the sum of x and +2 must =0 and/or the sum of x+3
must =0, or both sums could equal 0, thus the GENERAL solution set for
x of {x=-2, x=-3} dkw

.