1. **State the problem:** Expand and simplify the expression $$(5x+3)(-4x-3)$$. 2. **Use the distributive property (FOIL method):** Multiply each term in the first parenthesis by each term in the second. 3. Multiply the first terms: $$5x \times -4x = -20x^2$$. 4. Multiply the outer terms: $$5x \times -3 = -15x$$. 5. Multiply the inner terms: $$3 \times -4x = -12x$$. 6. Multiply the last terms: $$3 \times -3 = -9$$. 7. Combine all terms: $$-20x^2 - 15x - 12x - 9$$. 8. Combine like terms: $$-15x - 12x = -27x$$. 9. **Final simplified expression:** $$-20x^2 - 27x - 9$$.