Solve Zero Product 569B7F

1. **State the problem:** We need to find the values of $x$ that satisfy the equation $$(x - m)(x + n) = 0$$. 2. **Recall the zero product property:** If the 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 to the equation:** \begin{align*} (x - m)(x + n) &= 0 \\ \Rightarrow x - m &= 0 \quad \text{or} \quad x + n = 0 \end{align*} 4. **Solve each equation for $x$:** \begin{align*} x - m &= 0 \implies x = m \\ x + n &= 0 \implies x = -n \end{align*} 5. **Conclusion:** The values of $x$ that satisfy the equation are $$x = m$$ and $$x = -n$$. 6. **Match with the options given:** Option B: $m$ and $-n$. **Final answer:** Option B.