Solve the following quadratic equations by factorization:

We have been given

$6 x^{2}+11 x+3=0$

$6 x^{2}+9 x+2 x+3=0$

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

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

$2 x+3=0$

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

or,

$3 x+1=0$

$x=\frac{-1}{3}$

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