Solve the following quadratic equations by factorization:

We have been given

$5 x^{2}-3 x-2=0$

$5 x^{2}-5 x+2 x-2=0$

$5 x(x-1)+2(x-1)=0$

$(5 x+2)(x-1)=0$

Therefore,

$5 x+2=0$

$5 x=-2$

$x=\frac{-2}{5}$

or,

$x-1=0$

$x=1$

Hence, $x=\frac{-2}{5}$ or $x=1$.