1. **State the problem:** Solve the quadratic equation $$x(x-5)=0$$. 2. **Formula and rule:** The zero product property states that if $$ab=0$$, then either $$a=0$$ or $$b=0$$. 3. **Apply the zero product property:** Set each factor equal to zero: $$x=0$$ $$x-5=0$$ 4. **Solve each equation:** For $$x=0$$, the solution is $$x=0$$. For $$x-5=0$$, add 5 to both sides: $$x-5+5=0+5$$ $$\cancel{x}-\cancel{5}+5=5$$ $$x=5$$ 5. **Final answer:** The solutions to the equation $$x(x-5)=0$$ are $$x=0$$ and $$x=5$$.