1. **State the problem:** Solve the equation $1 (2 - y)^2 = -3y (2 - y)$ for $y$. 2. **Rewrite the equation:** $$ (2 - y)^2 = -3y (2 - y) $$ 3. **Expand the left side:** $$ (2 - y)^2 = (2 - y)(2 - y) = 4 - 4y + y^2 $$ 4. **Rewrite the right side:** $$ -3y (2 - y) = -6y + 3y^2 $$ 5. **Set the equation:** $$ 4 - 4y + y^2 = -6y + 3y^2 $$ 6. **Bring all terms to one side:** $$ 4 - 4y + y^2 + 6y - 3y^2 = 0 $$ 7. **Combine like terms:** $$ 4 + 2y - 2y^2 = 0 $$ 8. **Rewrite:** $$ -2y^2 + 2y + 4 = 0 $$ 9. **Divide entire equation by -2 to simplify:** $$ \cancel{-2}y^2 + \cancel{-2}y + \cancel{-2} \times 2 = 0 \Rightarrow y^2 - y - 2 = 0 $$ 10. **Factor the quadratic:** $$ (y - 2)(y + 1) = 0 $$ 11. **Solve for $y$:** $$ y - 2 = 0 \Rightarrow y = 2 $$ $$ y + 1 = 0 \Rightarrow y = -1 $$ **Final answer:** $y = 2$ or $y = -1$