$(2x+1)(\frac{5x-2}{3}-\frac{5-3x}{2})=0$
$⇔(2x+1)(\frac{10x-4-15+9x}{6})=0$
$⇔\left[ \begin{array}{l}2x+1=0\\\frac{10x-4-15+9x}{6}=0\end{array} \right.⇔\left[ \begin{array}{l}2x=-1\\10x-4-15+9x=0\end{array} \right.⇔\left[ \begin{array}{l}x=\frac{-1}{2}\\x=1\end{array} \right.$
Vậy $S=\{\frac{-1}{2};1\}$.