Answer
$x=-2$ and $x=3$.
Work Step by Step
The given equation is
$\Rightarrow 5x^2-5x-30=0$
Factor out $5$.
$\Rightarrow 5(x^2-x-6)=0$
Divide each side by $5$.
$\Rightarrow \frac{5(x^2-x-6)}{5}=\frac{0}{5}$
Simplify.
$\Rightarrow x^2-x-6=0$
Rewrite $-x$ as $2x-3x$.
$\Rightarrow x^2+2x-3x-6=0$
Group the terms.
$\Rightarrow (x^2+2x)+(-3x-6)=0$
Factor each group.
$\Rightarrow x(x+2)-3(x+2)=0$
Factor out $(x+2)$.
$\Rightarrow (x+2)(x-3)=0$
Use zero product property.
$\Rightarrow x+2=0$ or $x-3=0$
Solve for $x$.
$\Rightarrow x=-2$ or $x=3$
Hence, the solutions are $x=-2$ and $x=3$.
