Simplfiying $x(5xy+2x-1)=y(5xy+2y-1)$ I want to simplify: $x(5xy+2x-1)=y(5xy+2y-1)$ to $(x-y)(5xy+something-1)=0$ but I can't figure out what to do with the $2x$ and $2y$ on both sides.

\begin{eqnarray}
&&x(5xy+2x-1)=y(5xy+2y-1)\\
&\Rightarrow&(5x^2y-5xy^2)+(2x^2-2y^2)-(x-y)=0\\
&\Rightarrow&5xy(x-y)+2(x-y)(x+y)-(x-y)=0\\
&\Rightarrow&(x-y)(5xy+2x+2y-1)=0
\end{eqnarray}
Moreover, note that $5xy+2x+2y-1=5(x+\frac{2}{5})(y+\frac{2}{5})-\frac{9}{5}$, you can simplifying as following (if you want):
$(x-y)[(x+\frac{2}{5})(y+\frac{2}{5})-\frac{9}{25}]=0$.
