Expanding the given equation, we get:

(x^2+4x)^2 + 7x^2 + 28x + 12 = x^4 + 8x^3 + 16x^2 + 7x^2 + 28x + 12
= x^4 + 8x^3 + 23x^2 + 28x + 12

Now, we need to solve this equation for x.