To solve this equation, we need to simplify and expand each side.

First, let's expand the left side:

(6x - 1)(x + 1) = 6x^2 + 6x - x - 1 = 6x^2 + 5x - 1

(2x + 3)(3x - 2) = 6x^2 - 4x + 9x - 6 = 6x^2 + 5x - 6

Now, substitute these values back into the equation:

(6x^2 + 5x - 1) - (6x^2 + 5x - 6) = -3 + x

Simplify the equation:

6x^2 + 5x - 1 - 6x^2 - 5x + 6 = -3 + x

5 = -3 + x

Now, move -3 to the other side:

x = 5 - 3

x = 2

Therefore, the solution to the equation is x = 2.