1. **State the problem:** Solve the quadratic equation $$x^2 - 4x - 12 = 0$$ by factoring. 2. **Recall the factoring method:** To solve by factoring, we express the quadratic in the form $$ax^2 + bx + c = 0$$ and factor it into two binomials $$(x + m)(x + n) = 0$$ where $m$ and $n$ satisfy: - $m + n = b$ - $m \times n = c$ 3. **Identify coefficients:** Here, $a=1$, $b=-4$, and $c=-12$. 4. **Find two numbers that multiply to $-12$ and add to $-4$:** - Possible pairs: $(6, -2)$, $(-6, 2)$, $(4, -3)$, $(-4, 3)$, etc. - Check sums: - $6 + (-2) = 4$ (not $-4$) - $-6 + 2 = -4$ (correct) 5. **Write the factored form:** $$x^2 - 4x - 12 = (x - 6)(x + 2) = 0$$ 6. **Solve each factor for zero:** - $x - 6 = 0 \Rightarrow x = 6$ - $x + 2 = 0 \Rightarrow x = -2$ 7. **Final answer:** $$\boxed{x = 6 \text{ or } x = -2}$$