1. **Problem:** Factor the expression $5n^2 + 20n - 60$ completely. 2. **Step 1: Identify the greatest common factor (GCF).** The terms are $5n^2$, $20n$, and $-60$. The GCF is $5$. 3. **Step 2: Factor out the GCF.** $$5n^2 + 20n - 60 = 5(n^2 + 4n - 12)$$ 4. **Step 3: Factor the quadratic inside the parentheses.** We look for two numbers that multiply to $-12$ and add to $4$. These numbers are $6$ and $-2$. 5. **Step 4: Write the factored form.** $$5(n^2 + 4n - 12) = 5(n + 6)(n - 2)$$ 6. **Answer:** $$\boxed{5(n + 6)(n - 2)}$$ This completes the factoring of the first expression.