#### Answer

The solutions are $x=2$ and $x=-\dfrac{5}{6}$

#### Work Step by Step

$-6x^{2}+7x=-10$
Take all terms to the right side of the equation:
$0=6x^{2}-7x-10$
Rearrange:
$6x^{2}-7x-10=0$
Factor the left side of the equation:
$(6x+5)(x-2)=0$
Using the zero-factor property, set both factors equal to $0$ and solve each individual equation for $x$:
$6x+5=0$
$6x=-5$
$x=-\dfrac{5}{6}$
$x-2=0$
$x=2$
The solutions are $x=2$ and $x=-\dfrac{5}{6}$