1. **State the problem:** Solve the equation $$x^2 - 9 = 0$$ by factoring. 2. **Formula and rules:** To solve quadratic equations by factoring, we rewrite the equation in the form $$ax^2 + bx + c = 0$$ and factor the quadratic expression into two binomials. Then, we use the zero product property: if $$AB = 0$$, then $$A = 0$$ or $$B = 0$$. 3. **Factor the equation:** Recognize that $$x^2 - 9$$ is a difference of squares: $$x^2 - 9 = (x - 3)(x + 3)$$ 4. **Apply zero product property:** $$(x - 3)(x + 3) = 0$$ implies $$x - 3 = 0 \quad \text{or} \quad x + 3 = 0$$ 5. **Solve each equation:** $$x - 3 = 0 \Rightarrow x = 3$$ $$x + 3 = 0 \Rightarrow x = -3$$ 6. **Final answer:** $$x = 3 \quad \text{or} \quad x = -3$$