1. **State the problem:** Simplify the expression $4(5n - 2) - 3(4n + 5)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4(5n - 2) = 4 \times 5n - 4 \times 2 = 20n - 8$$ $$-3(4n + 5) = -3 \times 4n - 3 \times 5 = -12n - 15$$ 3. **Combine the results:** $$20n - 8 - 12n - 15$$ 4. **Group like terms:** $$ (20n - 12n) + (-8 - 15)$$ 5. **Simplify each group:** $$8n - 23$$ **Final answer:** $$8n - 23$$