1. The problem is to solve the equation using the Zero-Product Property: $$(x + 7)(4x - 5) = 0$$ 2. The Zero-Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. So, we set each factor equal to zero: $$x + 7 = 0$$ $$4x - 5 = 0$$ 3. Solve each equation separately. For $$x + 7 = 0$$: $$x = -7$$ For $$4x - 5 = 0$$: Add 5 to both sides: $$4x - 5 + 5 = 0 + 5$$ $$4x = 5$$ Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} = \frac{5}{4}$$ $$x = \frac{5}{4}$$ 4. Therefore, the solutions are: $$x = -7$$ and $$x = \frac{5}{4}$$