1. **State the problem:** Solve for $x$ in the equation $$(x - 3)(x - 8) = 0.$$\n\n2. **Formula and rule:** If a product of two factors equals zero, then at least one of the factors must be zero. This is called the Zero Product Property.\n\n3. **Apply the Zero Product Property:** Set each factor equal to zero:\n$$x - 3 = 0$$\nand\n$$x - 8 = 0.$$\n\n4. **Solve each equation:**\nFor $x - 3 = 0$, add 3 to both sides:\n$$x = 3.$$\nFor $x - 8 = 0$, add 8 to both sides:\n$$x = 8.$$\n\n5. **Final answer:** The two possible values of $x$ are $3$ and $8$.\n\n**Answer:** $3, 8$