Answer
$\{-5,2\}$.
Work Step by Step
The given equation is
$\Rightarrow 26-11x=16-8x+x^2$
Add $-26+11x$ to both sides.
$\Rightarrow 26-11x-26+11x=16-8x+x^2-26+11x$
Simplify.
$\Rightarrow 0=x^2+3x-10$
Rewrite the middle term $3x$ as $5x-2x$.
$\Rightarrow 0=x^2+5x-2x-10$
Group the terms.
$\Rightarrow 0=(x^2+5x)+(-2x-10)$
Factor each group.
$\Rightarrow 0=x(x+5)-2(x+5)$
Factor out $(x+5)$.
$\Rightarrow 0=(x+5)(x-2)$
By using zero product rule set each factor equal to zero.
$\Rightarrow x+5=0$ or $x-2=0$
Isolate $x$.
$\Rightarrow x=-5$ or $x=2$
The solution set is $\{-5,2\}$.
