1. **Problem Statement:** Find the equilibrium price and quantity for the commodity with supply function $P_s = Q^2 + 6Q + 9$ and demand function $P_d = Q^2 - 10Q + 25$. 2. **Formulas and Rules:** The market equilibrium occurs where supply equals demand, i.e., $P_s = P_d$. 3. **Set the equations equal:** $$Q^2 + 6Q + 9 = Q^2 - 10Q + 25$$ 4. **Simplify by subtracting $Q^2$ from both sides:** $$6Q + 9 = -10Q + 25$$ 5. **Bring all terms to one side:** $$6Q + 10Q = 25 - 9$$ $$16Q = 16$$ 6. **Solve for $Q$:** $$Q = \frac{16}{16} = 1$$ 7. **Find equilibrium price by substituting $Q=1$ into either function:** Using supply function: $$P_s = 1^2 + 6(1) + 9 = 1 + 6 + 9 = 16$$ 8. **Interpretation:** The equilibrium quantity is $Q=1$ and the equilibrium price is $P=16$. 9. **Graphical check:** Both curves intersect at $Q=1, P=16$ over the interval $0 \leq Q \leq 5$. **Final answer:** Equilibrium quantity $Q=1$, equilibrium price $P=16$.