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