To solve this equation, we need to simplify and then isolate the variable.

First, let's simplify the left side of the equation:

10x/2 - (2x+2)(2x-1) = 31
5x - (4x^2 - 2x + 4x - 2) = 31
5x - (4x^2 + 2x - 2) = 31
5x - 4x^2 - 2x + 2 = 31
5x - 2x - 4x^2 + 2 = 31
3x - 4x^2 + 2 = 31

Now, let's set the equation equal to zero:

3x - 4x^2 + 2 = 31
-4x^2 + 3x + 2 - 31 = 0
-4x^2 + 3x - 29 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve it, you can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = -4, b = 3, and c = -29. Plugging in these values, we get:

x = (-(3) ± sqrt((3)^2 - 4(-4)(-29))) / 2(-4)
x = (-3 ± sqrt(9 - 464)) / -8
x = (-3 ± sqrt(-455)) / -8

Since the square root of a negative number results in an imaginary number, the solution to this equation will also be complex.