#### Answer

The solutions are $x=1$ and $x=-\dfrac{2}{5}$

#### Work Step by Step

$5x^{2}-3x-2=0$
Factor the left side of the equation:
$(5x+2)(x-1)=0$
Using the zero-factor property, set both factors equal to $0$ and solve each individual equation for $x$:
$5x+2=0$
$5x=-2$
$x=-\dfrac{2}{5}$
$x-1=0$
$x=1$
The solutions are $x=1$ and $x=-\dfrac{2}{5}$