\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