Answer
$\left\{1,\frac{5}{2}\right\}$.
Work Step by Step
Add $-7x+5$ to both sides of the given equation.
$2x^2-7x+5=7x-5-7x+5$
Add like terms.
$2x^2-7x+5=0$
Rewrite the middle term $-7x$ as $-5x-2x$.
$2x^2-5x-2x+5=0$
Group terms.
$(2x^2-5x)+(-2x+5)=0$
Factor each term.
$x(2x-5)-1(2x-5)=0$
Factor out $(2x-5)$.
$(2x-5)(x-1)=0$
Plug each factor equal to zero.
$2x-5=0$ or $x-1=0$
Isolate $x$.
$x=\frac{5}{2}$ or $x=1$.
The solution set is $\left\{1,\frac{5}{2}\right\}$.
