Solve the following quadratic equations by factorization:

We have been given,

$(2 x+3)(3 x-7)=0$

Therefore,

$(2 x+3)=0$

$2 x=-3$

$x=\frac{-3}{2}$

or

$(3 x-7)=0$

$3 x=7$

$x=\frac{7}{3}$

Therefore, $x=\frac{-3}{2}$ or $x=\frac{7}{3}$.