(x + 2)(x + 3) + (x - 3)(x - 2) - 2(x + 1) = 0
(x^2 + 5x + 6) + (x^2 - 5x + 6) - (2x + 2) = 0
x^2 + 5x + 6 + x^2 - 5x + 6 - 2x - 2 = 0
x^2 + x^2 + 5x - 5x - 2x + 6 + 6 - 2 = 0
2x^2 - 2x + 10 = 0
2(x^2 - x + 5) = 0
x^2 - x + 5 = 0
(x^2 - x) + 5 = 0
(x - (1/2))^2 - (1/4) + 5 = 0
(x - (1/2))^2 + (19/4) = 0
(x - (1/2))^2 = -19/4
x - (1/2) = sqrt(-19/4) or = -sqrt(-19/4)
x = 1/2 + sqrt(-19/4) or x = 1/2 - sqrt(-19/4)
Note that there are no real answers, and there are only two complex answers.