1. **State the problem:** Solve the equation $$7c + 3(c - 5) = 2(c + 3) - 14$$ for $c$. 2. **Expand both sides:** $$7c + 3c - 15 = 2c + 6 - 14$$ 3. **Combine like terms:** $$10c - 15 = 2c - 8$$ 4. **Isolate variable terms on one side:** $$10c - 2c = -8 + 15$$ 5. **Simplify both sides:** $$8c = 7$$ 6. **Solve for $c$ by dividing both sides by 8:** $$c = \frac{7}{8}$$ 7. **Answer:** The solution is $c = \frac{7}{8}$, which corresponds to Option D.