$4x^3+23x^2-2x=0\\x(4x^2+23x-2)=0$

By Zero Product Property:
$x=0\ \ \text{or}\ \ 4x^2+23\ x-2=0$

By the Quadratic Formula:
$x=\frac{-23\pm\sqrt{23^{2}-4(4)(-2)}}{2(4)}$
Now solve for the remaining two $x$-values.