To solve the equation \( x^2 - 9 = 3(x + 3) \), follow these steps:

1. **Distribute the 3 on the right side**:
\[
3(x + 3) = 3x + 9
\]
So, the equation becomes:
\[
x^2 - 9 = 3x + 9
\]

2. **Rearrange the equation** by moving all terms to one side:
\[
x^2 - 3x - 9 - 9 = 0
\]
Simplifying this gives:
\[
x^2 - 3x - 18 = 0
\]

3. **Factor the quadratic equation**:
We need two numbers that multiply to \(-18\) and add to \(-3\). The numbers are \(-6\) and \(3\):
\[
(x - 6)(x + 3) = 0
\]

4. **Set each factor to zero**:
\[
x - 6 = 0 \quad \text{or} \quad x + 3 = 0
\]
This gives us:
\[
x = 6 \quad \text{or} \quad x = -3
\]

The solutions to the equation are \( x = 6 \) and \( x = -3 \).