I recognize that this is a quadratic equation, and I know that the product of two factors is zero only when one or both of them are zero. So, I can find the solutions by setting each factor equal to zero and solving for x. For the first factor, I get $3x+5 = 0$, which implies that $x = -\frac{5}{3}$. For the second factor, I get $2x-9 = 0$, which implies that $x = \frac{9}{2}$. These are the two solutions for x, and the question asks for their sum. To add two fractions, I need to have a common denominator, so I multiply the first fraction by $\frac{2}{2}$ and the second fraction by $\frac{3}{3}$. This gives me $-\frac{10}{6} + \frac{27}{6} = \frac{17}{6}$. 
What is the sum of the solutions of the equation $(3x+5)(2x-9) = 0$? Express your answer as a common fraction.