Answer
$\{-5,\frac{1}{2}\}$.
Work Step by Step
Subtract $5$ from both sides of the given equation.
$\Rightarrow 2x^2+9x-5=5-5$
Simplify.
$\Rightarrow 2x^2+9x-5=0$
Rewrite the middle term $9x$ as $10x-1x$.
$\Rightarrow 2x^2+10x-1x-5=0$
Group the terms.
$\Rightarrow (2x^2+10x)+(-1x-5)=0$
Factor each group.
$\Rightarrow 2x(x+5)-1(x+5)=0$
Factor out $(x+5)$
$\Rightarrow (x+5)(2x-1)=0$
Set each factor equal to zero.
$\Rightarrow x+5=0$ or $2x-1=0$
Isolate $x$.
$\Rightarrow x=-5$ or $x=\frac{1}{2}$
The solution set is $\{-5,\frac{1}{2}\}$.
