(2x-3)(2x-1)(x+1)(x+2)=36

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To solve this equation, we first need to expand the left side of the equation by using the distributive property.

(2x-3)(2x-1)(x+1)(x+2)
= (2x-3)(2x^2 +4x - x -1)(x+2)
= (2x-3)(2x^2 + 3x -1)(x+2)
= 2x(2x^2 + 3x - 1) - 3(2x^2 + 3x - 1)(x+2)
= 4x^3 + 6x^2 - 2x - 6x^2 - 9x + 3 - 3(2x^2 + 3x - 1)(x+2)
= 4x^3 - 9x + 3 - 6x^2 - 9x + 3 - 3(2x^2 + 3x - 1)(x+2)
= 4x^3 - 6x^2 - 18x + 6 - 6x^2 - 9x + 3 - 6x^3 - 9x^2 + 3x + 4
= -6x^3 - 3x + 13

Now set this expression equal to 36:
-6x^3 - 3x + 13 = 36
-6x^3 - 3x + 13 - 36 = 0
-6x^3 - 3x - 23 = 0

This is the final equation obtained after solving for the given equation.