2x^2 - 19x - 33 = 0
The factors of 2 are 1 x 2.
The factors of 33 are 1 x 33 and 3 x 11.
Using Guess and Test and FOIL, find a combination that gives you a middle term of -19x:
(2x + 3)(x - 11) = 0.
Using the principal of zero product, solve each equation for x:
2x + 3 =0 and x - 11 =0.
The two solutions are x = -3/2 and x = 11.