Here you have a quadratic equation with one unknown variable (x). Since the equation is set equal to 0, we solve for it by factoring the left hand side of the equation and then apply the zero product property to solve for the unknown variable (x).
Factoring: 2x2 + 3x - 2 = 0
(2x - 1)(x + 2) = 0
Zero product property: (2x - 1)(x + 2) = 0
2x - 1 = 0 AND x + 2 = 0
2x - 1 = 0 AND x + 2 = 0
+ 1 + 1 - 2 - 2
______________ _______________
2x = 1 x = -2
(2x) / 2 = (1) / 2
x = 1/2
Thus, the solution to this equation is: x = 1/2 and x = -2