To solve this quadratic equation, let's first simplify it by expanding the expressions:

(x^2 + x)^2 - 5(x^2 + x) + 6 = 0

Expanding the squared term (x^2 + x)^2:

(x^4 + 2x^3 + x^2) - 5(x^2 + x) + 6 = 0

Now simplify by combining like terms:

x^4 + 2x^3 + x^2 - 5x^2 - 5x + 6 = 0

x^4 + 2x^3 - 4x^2 - 5x + 6 = 0

Now, you can try factoring or using the quadratic formula to find the solutions to this equation.