To solve this equation, we first distribute the terms in the equation to expand and simplify:

(x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1

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

Now we can rewrite the original equation with the expanded terms:

(x^2 + 2x + 1)(x^2 + 2x) = 12

Next, multiply the binomials together:

x^4 + 2x^3 + x^2 + 2x^3 + 4x^2 + 2x = 12

Combine like terms:

x^4 + 4x^3 + 5x^2 + 2x = 12

Now we have a quadratic equation that can be simplified further by setting it equal to 0 and factoring or using the quadratic formula.