Solve each of the following quadratic equations:

$(2 x-3)(3 x+1)=0$

$\Rightarrow 2 x-3=0$ or $3 x+1=0$

$\Rightarrow 2 x=3$ or $3 x=-1$

$\Rightarrow x=\frac{3}{2}$ or $x=-\frac{1}{3}$

Hence, the roots of the given equation are $\frac{3}{2}$ and $-\frac{1}{3}$.