\(\begin{align}
  & x\left( x+1 \right)=y\left( y+1 \right)\left( {{y}^{2}}+1 \right) \\
& \left( x,y \right)=\left( 0,0 \right),\left( 0,-1 \right),\left( -1,0 \right),\left( -1,-1 \right) \\
&  \\
& {{x}^{2}}+x-\left( {{y}^{2}}+y \right)\left( {{y}^{2}}+1 \right)=0 \\
& \left[ x+\left( {{y}^{2}}+y \right) \right]\left[ x-\left( {{y}^{2}}+1 \right) \right]=0 \\
& {{y}^{2}}+y={{y}^{2}}+1+1 \\
& y=2 \\
& \left( x,y \right)=\left( 5,2 \right),\left( -6,2 \right) \\
\end{align}\)

常數項\(\left( {{y}^{2}}+y \right)\left( {{y}^{2}}+1 \right)\)拆成\(\left( {{y}^{2}}+y \right)\)和\(\left( {{y}^{2}}+1 \right)\)相乘
要配出x項係數1，故\(\left( {{y}^{2}}+y \right)\)比\(\left( {{y}^{2}}+1 \right)\)大1