1. **State the problem:** Solve the equation $Y(3+y)=0$ for $y$. 2. **Formula and rules:** The product of two factors equals zero if and only if at least one of the factors is zero. This is called the zero product property. 3. **Apply the zero product property:** Set each factor equal to zero: $$Y=0$$ or $$3+y=0$$ 4. **Solve each equation:** - From $Y=0$, we get $Y=0$ (if $Y$ is a variable or constant, this is one solution). - From $3+y=0$, subtract 3 from both sides: $$3+\cancel{y}=0\Rightarrow \cancel{3}+y=-3$$ which simplifies to $$y=-3$$ 5. **Final answer:** The solutions are $Y=0$ or $y=-3$. If $Y$ is a constant and not a variable, then the only solution for $y$ is $-3$.