Expanding the equation:
(x-2)(x-3) - (x+2)(x-5) = 2
(x^2 - 3x - 2x + 6) - (x^2 - 5x + 2x - 10) = 2
(x^2 - 5x + 6) - (x^2 - 3x - 10) = 2
x^2 - 5x + 6 - x^2 + 3x + 10 = 2
-2x + 16 = 2
-2x = -14
x = 7
Therefore, the solution to the equation is x = 7.
Expanding the equation:
(x-2)(x-3) - (x+2)(x-5) = 2
(x^2 - 3x - 2x + 6) - (x^2 - 5x + 2x - 10) = 2
(x^2 - 5x + 6) - (x^2 - 3x - 10) = 2
x^2 - 5x + 6 - x^2 + 3x + 10 = 2
-2x + 16 = 2
-2x = -14
x = 7
Therefore, the solution to the equation is x = 7.