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.