1. **Problem:** Solve the quadratic equation $x^2 + x - 6 = 0$ by factoring. 2. **Formula and rules:** To solve quadratic equations by factoring, we look for two numbers that multiply to the constant term and add to the coefficient of $x$. 3. **Step 1: Factor the quadratic.** $$x^2 + x - 6 = (x + 3)(x - 2) = 0$$ 4. **Step 2: Set each factor equal to zero.** $$x + 3 = 0 \quad \text{or} \quad x - 2 = 0$$ 5. **Step 3: Solve each equation.** $$x = -3 \quad \text{or} \quad x = 2$$ 6. **Answer:** The solutions are $x = -3$ and $x = 2$. This is the first problem solved in detail as requested.