Answer
$\{-5,0,2\}$.
Work Step by Step
Subtract $20x$ from both sides of the given equation.
$2x^3+6x^2-20x=20x-20x$
Add like terms.
$2x^3+6x^2-20x=0$
Factor out $2x$ from all terms.
$2x(x^2+3x-10)=0$
Rewrite the middle term $3x$ as $5x-2x$.
$2x(x^2+5x-2x-10)=0$
Group terms.
$2x[(x^2+5x)+(-2x-10)]=0$
Factor each term.
$2x[x(x+5)-2(x+5)]=0$
Factor out $(x+5)$.
$2x(x+5)(x-2)=0$
Plug each factor equal to zero.
$2x=0 $ or $x+5=0$ or $x-2=0$
Isolate $x$.
$x=0$ or $x=-5$ or $x=2$.
The solution set is $\{-5,0,2\}$.
