1. **State the problem:** Solve the equation $x(x-3)=0$ for $x$. 2. **Formula and rule:** The zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. That is, if $ab=0$, then either $a=0$ or $b=0$. 3. **Apply the zero product property:** Here, the factors are $x$ and $(x-3)$. So, set each factor equal to zero: $$x=0$$ and $$x-3=0$$ 4. **Solve each equation:** - For $x=0$, the solution is $x=0$. - For $x-3=0$, add 3 to both sides: $$x-3+3=0+3$$ $$\cancel{x-3}+3=\cancel{0}+3$$ $$x=3$$ 5. **Final answer:** The solutions to the equation $x(x-3)=0$ are $$x=0 \text{ or } x=3$$