To solve the equation, we can start by expanding the square:

(x + 3)^2 - 9 = 0
(x + 3)(x + 3) - 9 = 0
(x^2 + 6x + 9) - 9 = 0
x^2 + 6x = 0

Next, we can factor out an x:

x(x + 6) = 0

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

x = 0 or x + 6 = 0

For x = 0, the equation is satisfied. For x + 6 = 0, we subtract 6 from both sides:

x = -6

Therefore, the solutions to the equation (x + 3)^2 - 9 = 0 are x = 0 and x = -6.