1. The problem asks us to solve the equation using the Zero-Product Property: $$(3x - 7)(2x + 1) = 0$$ 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: $$3x - 7 = 0$$ $$2x + 1 = 0$$ 3. Solve the first equation: $$3x - 7 = 0$$ Add 7 to both sides: $$3x = 7$$ Divide both sides by 3: $$x = \frac{7}{3}$$ 4. Solve the second equation: $$2x + 1 = 0$$ Subtract 1 from both sides: $$2x = -1$$ Divide both sides by 2: $$x = \frac{-1}{2}$$ 5. Therefore, the solutions are: $$x = \frac{7}{3} \text{ and } x = -\frac{1}{2}$$