1. **State the problem:** Solve the equation $$y^2 = 9y$$ for $y$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$y^2 - 9y = 0$$ 3. **Factor the equation:** Factor out the common factor $y$: $$y(y - 9) = 0$$ 4. **Apply the zero product property:** For the product to be zero, either factor must be zero: $$y = 0 \quad \text{or} \quad y - 9 = 0$$ 5. **Solve each equation:** - If $y = 0$, then $y = 0$. - If $y - 9 = 0$, then $y = 9$. 6. **Final answer:** The solutions to the equation are: $$y = 0 \quad \text{or} \quad y = 9$$