1. **State the problem:** Simplify the expression $$(7c + 2)(6c + 3) - (5c - 2).$$ 2. **Use the distributive property (FOIL) to expand the first product:** $$(7c + 2)(6c + 3) = 7c \times 6c + 7c \times 3 + 2 \times 6c + 2 \times 3 = 42c^2 + 21c + 12c + 6 = 42c^2 + 33c + 6.$$ 3. **Rewrite the expression with the expanded product:** $$42c^2 + 33c + 6 - (5c - 2).$$ 4. **Distribute the minus sign to the second parentheses:** $$42c^2 + 33c + 6 - 5c + 2.$$ 5. **Combine like terms:** $$42c^2 + (33c - 5c) + (6 + 2) = 42c^2 + 28c + 8.$$ **Final answer:** $$42c^2 + 28c + 8.$$