1. **State the problem:** Solve the equation $ (3x - 4)(2x - 13) = 0 $. 2. **Formula and rule:** The zero product property states that if $ab = 0$, then either $a = 0$ or $b = 0$. This means we can set each factor equal to zero and solve separately. 3. **Set each factor to zero:** $$ 3x - 4 = 0 $$ $$ 2x - 13 = 0 $$ 4. **Solve the first equation:** $$ 3x - 4 = 0 $$ Add 4 to both sides: $$ 3x = 4 $$ Divide both sides by 3: $$ x = \frac{\cancel{3}x}{\cancel{3}} = \frac{4}{3} $$ 5. **Solve the second equation:** $$ 2x - 13 = 0 $$ Add 13 to both sides: $$ 2x = 13 $$ Divide both sides by 2: $$ x = \frac{\cancel{2}x}{\cancel{2}} = \frac{13}{2} $$ 6. **Final answer:** The solutions to the equation are $$ x = \frac{4}{3} \quad \text{or} \quad x = \frac{13}{2} $$