1. **State the problem:** Solve the equation $ (x + 7)(4x - 5) = 0 $ using the Zero-Product Property. 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 $AB = 0$, then either $A = 0$ or $B = 0$. 3. **Apply the property:** Set each factor equal to zero: $$ x + 7 = 0 $$ $$ 4x - 5 = 0 $$ 4. **Solve each equation:** For $x + 7 = 0$: $$ x = -7 $$ For $4x - 5 = 0$: $$ 4x = 5 $$ $$ \cancel{4}x = \cancel{4} \frac{5}{4} $$ $$ x = \frac{5}{4} $$ 5. **Final answer:** $$ x = -7 \quad \text{and} \quad x = \frac{5}{4} $$ These are the solutions to the equation using the Zero-Product Property.