Answer
$x=0$ or $x=\pm\sqrt{2}$
Work Step by Step
We solve by factoring out $6x$:
$6x^{5}-24x=0$
$6x(x^{4}-4)=0$
$6x(x^{2}+2)(x^{2}-2)=0$
$6x=0$ or $x^2+2=0$ or $x^2-2=0$
$x=0$ or $x=\pm\sqrt{2}$
(The middle equation, $x^2+2=0$ has no real solution.)
