To solve this equation, we need to expand the left side and then set it equal to 0:

(4x + 4)^2 = 0
16x^2 + 32x + 16 = 0

Now, we can solve this quadratic equation by factoring:

16x^2 + 32x + 16 = 0
16(x^2 + 2x + 1) = 0
16(x + 1)^2 = 0

Now we can set the factor equal to zero and solve for x:

(x + 1)^2 = 0
x + 1 = 0
x = -1

Therefore, x = -1 is the solution to the equation (4x + 4)^2 = 0.