1. **Problem statement:** Solve the equation $x \cdot (x - 2) = 0$. 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 $a \cdot b = 0$, then either $a = 0$ or $b = 0$. 3. **Apply the zero product property:** Set each factor equal to zero: $$x = 0$$ and $$x - 2 = 0$$ 4. **Solve each equation:** For $x = 0$, the solution is $x = 0$. For $x - 2 = 0$, add 2 to both sides: $$x - 2 + 2 = 0 + 2$$ $$\cancel{x - 2} + 2 = \cancel{0} + 2$$ $$x = 2$$ 5. **Final solution:** The solutions to the equation are $x = 0$ and $x = 2$. These are the points where the product equals zero, meaning the original equation holds true.