To solve the equation \((-3x + \frac{1}{2})(x^2 - \frac{9}{10}) = 0\), we set each factor equal to zero and solve for \(x\).

1. **First Factor**: \(-3x + \frac{1}{2} = 0\)

\[
-3x = -\frac{1}{2}
\]
\[
x = \frac{1}{2} \div 3 = \frac{1}{6}
\]

2. **Second Factor**: \(x^2 - \frac{9}{10} = 0\)

\[
x^2 = \frac{9}{10}
\]
\[
x = \pm \sqrt{\frac{9}{10}} = \pm \frac{3}{\sqrt{10}} = \pm \frac{3\sqrt{10}}{10}
\]

Thus, the complete solution set for the equation \((-3x + \frac{1}{2})(x^2 - \frac{9}{10}) = 0\) is:

\[
x = \frac{1}{6}, \quad x = \frac{3\sqrt{10}}{10}, \quad x = -\frac{3\sqrt{10}}{10}
\]