Answer
Solutions:
$x=0$ and $x=\frac{12}{5}$
Work Step by Step
$5x^4-12x^3=0$
$x^3(5x-12)=0$
$x^3=0$
$x=0$
or
$5x-12=0$
$5x=12$
$x=\frac{12}{5}$
Testing:
- $x=0$:
$5(0)^4-12(0)^3=0-0=0$
- $x=\frac{12}{5}$:
$5(\frac{12}{5})^4-12(\frac{12}{5})^3=5\frac{12^4}{5^4}=12\frac{12^3}{5^3}=\frac{12^4}{5^3}-\frac{12^4}{5^3}=0$
