Let's first expand both sides of the equation:

Left side:
(х-2)(х+3) = х^2 + 3x - 2x - 6 = х^2 + x - 6

(х+2)^2 = (х+2)(х+2) = х^2 + 2x + 2x + 4 = х^2 + 4x + 4

Now substitute these back into the equation:

(х^2 + x - 6) - (х^2 + 4x + 4) = 2

Simplify the equation:

х + 2 = 2

Subtract 2 from both sides:

х = 0

Therefore, the solution to the equation is х = 0.