1. **State the problem:** Factor the quadratic expression $$4x^2 + 4x - 15$$. 2. **Recall the factoring formula:** For a quadratic $$ax^2 + bx + c$$, we look for two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Calculate the product and sum:** Here, $$a = 4$$, $$b = 4$$, and $$c = -15$$. Calculate $$a \times c = 4 \times (-15) = -60$$. We need two numbers that multiply to $$-60$$ and add to $$4$$. 4. **Find the pair:** The numbers $$10$$ and $$-6$$ work because $$10 \times (-6) = -60$$ and $$10 + (-6) = 4$$. 5. **Rewrite the middle term:** $$4x^2 + 10x - 6x - 15$$ 6. **Group terms:** $$(4x^2 + 10x) + (-6x - 15)$$ 7. **Factor each group:** $$2x(2x + 5) - 3(2x + 5)$$ 8. **Factor out the common binomial:** $$(2x - 3)(2x + 5)$$ **Final answer:** $$4x^2 + 4x - 15 = (2x - 3)(2x + 5)$$.