Solve the following quadratic equations by factorization:

We have been given

$3 x^{2}=-11 x-10$

$3 x^{2}+11 x+10=0$

$3 x^{2}+6 x+5 x+10=0$

$3 x(x+2)+5(x+2)=0$

$(3 x+5)(x+2)=0$

Therefore,

$3 x+5=0$

$3 x=-5$

$x=\frac{-5}{3}$

or,

$x+2=0$

$x=-2$

Hence, $x=\frac{-5}{3}$ or $x=-2$.