1. **State the problem:** Solve the equation $x(x + 5) - 12 = x^2 + 3x$. 2. **Write the equation:** $$x(x + 5) - 12 = x^2 + 3x$$ 3. **Expand the left side:** $$x^2 + 5x - 12 = x^2 + 3x$$ 4. **Subtract $x^2 + 3x$ from both sides to bring all terms to one side:** $$x^2 + 5x - 12 - x^2 - 3x = 0$$ 5. **Simplify:** $$2x - 12 = 0$$ 6. **Solve for $x$:** $$2x = 12$$ $$x = \frac{12}{2} = 6$$ 7. **Final answer:** $$x = 6$$