To solve the equation \( x(x + 2) = 3x + 6 \), follow these steps:

1. Expand the left-hand side of the equation:
\[
x(x + 2) = x^2 + 2x
\]

2. Rewrite the equation with the expanded form:
\[
x^2 + 2x = 3x + 6
\]

3. Move all terms to one side of the equation to set it to zero:
\[
x^2 + 2x - 3x - 6 = 0
\]

4. Combine like terms:
\[
x^2 - x - 6 = 0
\]

5. Factor the quadratic equation:
\[
x^2 - x - 6 = (x - 3)(x + 2) = 0
\]

6. Set each factor equal to zero and solve for \( x \):
\[
x - 3 = 0 \quad \text{or} \quad x + 2 = 0
\]

\[
x = 3 \quad \text{or} \quad x = -2
\]

So, the solutions to the equation \( x(x + 2) = 3x + 6 \) are \( x = 3 \) and \( x = -2 \).