Solve Equation 569193

1. **State the problem:** Solve the equation $$(x - 10)(x + 20) = 0$$ for $x$. 2. **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. 3. **Apply the Zero Product Property:** Set each factor equal to zero: $$x - 10 = 0$$ $$x + 20 = 0$$ 4. **Solve each equation:** For $$x - 10 = 0$$: Add 10 to both sides: $$x - 10 + 10 = 0 + 10$$ $$x = 10$$ For $$x + 20 = 0$$: Subtract 20 from both sides: $$x + 20 - 20 = 0 - 20$$ $$x = -20$$ 5. **Final answer:** The solutions to the equation are $$x = 10$$ and $$x = -20$$.