1. **State the problem:** Solve the equation $$0 = (x - 1)(x - 3)$$ for $x$. 2. **Recall the zero product property:** If a product of two factors equals 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: $$x - 1 = 0$$ $$x - 3 = 0$$ 4. **Solve each equation:** For $$x - 1 = 0$$: $$x = 1$$ For $$x - 3 = 0$$: $$x = 3$$ 5. **Final answer:** The solutions to the equation are $$x = 1$$ and $$x = 3$$.