2x^3 + 3x^2 - 8x = 12
this is a cubic equation so set f(x) = 2x^3 + 3x^2 - 8x - 12 = 0 and search for roots.
f(0) = -12, negative
f(1) = -15, more negative
f(2) = 16 + 12 - 16 - 12 = 0 -- a root has been found.
(x - 2) is a factor of f(x), so divide f(x) by (x-2), giving
(x - 2)(2x^2 + 7x + 6) = 0 and the quadratic here factorises to give,
(x - 2)(2x + 3)(x + 2) = 0
So the solutions are: x = 2, x = -3/2, x = -2