\(2xy+2x+y=-6\)
\(\Leftrightarrow2xy+2x+y+1=-6+1\)
\(\Leftrightarrow2x\left(y+1\right)+\left(y+1\right)=-5\)
\(\Leftrightarrow\left(2x+1\right)\left(y+1\right)=-5\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}2x+1=1\\y+1=-5\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=-1\\2x+1=5\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=-5\\y+1=1\end{matrix}\right.\\\left\{{}\begin{matrix}2x+1=5\\y+1=-1\end{matrix}\right.\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=0\\y=-6\end{matrix}\right.\\\left\{{}\begin{matrix}x=-1\\y=2\end{matrix}\right.\\\left\{{}\begin{matrix}x=-3\\y=0\end{matrix}\right.\\\left\{{}\begin{matrix}x=2\\y=-2\end{matrix}\right.\end{matrix}\right.\)
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