(x+1)(x^2+2)+(x+2)(x^2+1)=2

Question

(x+1)(x^2+2)+(x+2)(x^2+1)=2

Answer 1

(x^3 + x^2 + 2x + 2) + (x^3 + 2x^2 + x + 2) = 2
2x^3 + 3x^2 + 3x + 2 = 0
(x^3 + 1) + (x^3 + 3x^2 + 3x + 1) = 0
(x + 1)(x^2 - x + 1) + (x + 1)^3 = 0
(x + 1)(2x^2 + x + 2) = 0
x = -1