Answer
$\{-8,7\}$.
Work Step by Step
$x(x-2)+3(x-2)=50$
Use the distributive property.
$x^2-2x+3x-6=50$
Add like terms.
$x^2+x-6=50$
Subtract $50$ from both sides.
$x^2+x-6-50=50-50$
Add like terms.
$x^2+x-56=0$
Rewrite the middle term $x$ as $8x-7x$.
$x^2+8x-7x-56=0$
Group terms.
$(x^2+8x)+(-7x-56)=0$
Factor each term.
$x(x+8)-7(x+8)=0$
Factor out $(x+8)$.
$(x+8)(x-7)=0$
Set each factor equal to zero.
$x+8=0$ or $x-7=0$
Isolate $x$.
$x=-8$ or $x=7$.
The solution set is $\{-8,7\}$.
