Answer
Solutions:
$x=0$, $x=\frac{5}{3}$ and $x=-\frac{5}{3}$
Work Step by Step
$36x^3-100x=0$
$4x(9x^2-25)=0$
$4x=0$
$x=0$
or
$9x^2-25=0$
$9x^2=25$
$x^2=\frac{25}{9}$
$x=±\frac{5}{3}$
Testing:
$x=0$:
$36(0)^3-100(0)=0-0=0$
$x=\frac{5}{3}$:
$36(\frac{5}{3})^3-100(\frac{5}{3})=36~\frac{125}{27}-\frac{500}{3}=\frac{4500}{27}-\frac{500}{3}=\frac{500}{3}-\frac{500}{3}=0$
$x=-\frac{5}{3}$:
$36(-\frac{5}{3})^3-100(-\frac{5}{3})=36~(-\frac{125}{27})+\frac{500}{3}=-\frac{4500}{27}+\frac{500}{3}=-\frac{500}{3}+\frac{500}{3}=0$
