$$\left. \begin{array} { l } { x ^ { 2 } y ^ { 2 } + y ^ { 2 } + 6 x + 6 y = 0 - 2 x y + 6 x y - 1 / 20 x - 1 / 20 x - 1 / 2 x - 1 / 2 x } \\ { 4 x \text { c h e b e r \right.$$
$x=0\text{, }y=0\text{, }z=0$
$x=\frac{z}{4}\text{, }y\neq 0\text{, }z=\frac{\sqrt{5041-5680y+1600y^{2}-2400y^{3}-400y^{4}}+40y-71}{5y^{2}}$
$x=\frac{z}{4}\text{, }y\neq 0\text{, }z=\frac{-\sqrt{5041-5680y+1600y^{2}-2400y^{3}-400y^{4}}+40y-71}{5y^{2}}$
$\left\{\begin{matrix}\\x=0\text{, }y=0\text{, }z=0\text{, }&\text{unconditionally}\\x=\frac{z}{4}\text{, }y\in \mathrm{R}\text{, }z=\frac{\sqrt{5041-5680y+1600y^{2}-2400y^{3}-400y^{4}}+40y-71}{5y^{2}}\text{; }x=\frac{z}{4}\text{, }y\in \mathrm{R}\text{, }z=\frac{-\sqrt{5041-5680y+1600y^{2}-2400y^{3}-400y^{4}}+40y-71}{5y^{2}}\text{, }&y\neq 0\text{ and }5041-5680y+1600y^{2}-2400y^{3}-400y^{4}\geq 0\end{matrix}\right.$
