How can you use factoring to solve quadratic equations in standard form?

An example will illustrate one method of doing this. Its called the 'ac' method.

Solve  2x^2  - 3x -  20 = 0

multiply the first and last numbers:- 2 * -20  = -40

Note that -40 = -8 * 5    and  -8 + 5  = -3  ( the 'middle' number in the standard form)
so we write:-
2x^2 - 8x + 5x - 20 = 0
2x(x - 4) + 5(x - 4) = 0 
(2x + 5)(x - 4) = 0
giving 2x + 5 = 0  or x - 4 = 0
giving the roots  x = -2.5 and x = 4