x³ + 2x² - 9x = 18

x³ + 2x² - 9x - 18 = 0

Putting x=3, we find that it is one of the solutions.

Therefore,

(x-3)(x² + 5x + 6) = 0

x² + 5x + 6 = (x+3)(x+2)

Therfore,

(x-3)(x+3)(x+2) = 0

which gives the following values of x :- 3, -3, -2

PS:_ A cubic equation, that is an equation of degree three, can be solved only by trial and error, as far as I know.