How does $\frac{-1}{x^2}+2x=0$ become $2x^3-1=0$? Below is part of a solution to a critical points question. I'm just not sure how the equation on the left becomes the equation on the right. Could someone please show me the steps in-between? Thanks.

$$\frac{-1}{x^2}+2x=0 \implies 2x^3-1=0$$


The solution has multiplied both left and right side by $x^2$
Observe: 
\begin{align}
&-\frac{1}{x^2} * x^2 + 2x(x^2) = 0 * x^2 \\
&\implies -\frac{x^2}{x^2} + 2x^3 = 0 \\
&\implies -1 + 2x^3 = 0
\end{align}
