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

(x^2 + x)^2 = (x^2 + x)(x^2 + x)
= x^4 + x^3 + x^3 + x^2
= x^4 + 2x^3 + x^2

Now, let's distribute the -11 to the terms inside the parentheses:

11(x^2 + x) = 11x^2 + 11x

Substitute these back into the equation:

(x^2 + x)^2 - 11(x^2 + x) = x^4 + 2x^3 + x^2 - 11x^2 - 11x

Now, simplify and combine like terms:

x^4 + 2x^3 + x^2 - 11x^2 - 11x = x^4 + 2x^3 - 10x^2 - 11x

We want this to equal 12, so our equation becomes:

x^4 + 2x^3 - 10x^2 - 11x = 12

This is the final equation.