Answer
$\{2,5\}$
Work Step by Step
Use distributive property.
$\begin{align*}
2x(x)-2x(5)&=4(x)-4(5)\\
2x^2-10x&=4x-20
\end{align*}$
Add $-4x+20$ to both sides.
$2x^2-10x-4x+20=4x-20-4x+20$
Simplify.
$2x^2-14x+20=0$
Divide both sides of the equation by $2$.
$x^2-7x+10=0$
Rewrite $-7x$ as $-5x-2x$
$x^2-5x-2x+10=0$
Group the first two terms together and group the last two terms together.
$(x^2-5x)+(-2x+10)=0$
Factor out the GCF of each group.
$x(x-5)-2(x-5)=0$
Factor out $(x-5)$.
$(x-5)(x-2)=0$
Use Zero-Product Property.
$x-5=0$ or $x-2=0$
Solve each equation for $x$.
$x=5$ or $x=2$
Hence, the solution set of the equation is $\{2,5\}$.
