Answer
Solutions:
$x=0$ and $x=\frac{3}{2}$
Work Step by Step
$4x^3-6x^2=0$
$2x^2(2x-3)=0$
$2x^2=0$
$x^2=0$
$x=0$
or
$2x-3=0$
$2x=3$
$x=\frac{3}{2}$
Testing:
- $x=0$:
$4(0)^3-6(0)^2=0-0=0$
- $x=\frac{3}{2}$:
$4(\frac{3}{2})^3-6(\frac{3}{2})^2=4~\frac{27}{8}-6~\frac{9}{4}=\frac{108}{8}-\frac{54}{4}=\frac{27}{2}-\frac{27}{2}=0$
