Answer
$x=0$ or $x=\frac{1}{16}$
Work Step by Step
We solve by factoring:
$x-4x\sqrt{x}=0$
$x(1-4\sqrt{x})=0$
$x=0$ or $1-4\sqrt{x}=0$
$x=0$ or $1=4\sqrt{x}$
$x=0$ or $\frac{1}{4}=\sqrt{x}$
$x=0$ or $(\frac{1}{4})^{2}=(\sqrt{x})^{2}$
$x=0$ or $x=\frac{1}{16}$