1. **State the problem:** Factor the quadratic expression $$g^2 + 12g - 13$$. 2. **Recall the factoring formula:** For a quadratic expression $$ax^2 + bx + c$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Identify coefficients:** Here, $$a=1$$, $$b=12$$, and $$c=-13$$. 4. **Calculate product $$ac$$:** $$1 \times (-13) = -13$$. 5. **Find two numbers that multiply to $$-13$$ and add to $$12$$:** These numbers are $$13$$ and $$-1$$ because $$13 \times (-1) = -13$$ and $$13 + (-1) = 12$$. 6. **Rewrite the middle term using these numbers:** $$g^2 + 13g - 1g - 13$$. 7. **Group terms:** $$(g^2 + 13g) + (-1g - 13)$$. 8. **Factor each group:** $$g(g + 13) - 1(g + 13)$$. 9. **Factor out the common binomial:** $$(g + 13)(g - 1)$$. 10. **Final answer:** The factored form of $$g^2 + 12g - 13$$ is $$\boxed{(g + 13)(g - 1)}$$.