Løs 6m+18=n^2-2nm^2+4mn+10m+6n+10

$$6 m + 18 = n ^ { 2 } - 2 n m ^ { 2 } + 4 m n + 10 m + 6 n + 10$$

Løs for m (complex solution)

$$\left\{\begin{matrix}m=\frac{\sqrt{2n^{3}+16n^{2}-8n+4}}{2n}+1+\frac{1}{n}\text{; }m=-\frac{\sqrt{2n^{3}+16n^{2}-8n+4}}{2n}+1+\frac{1}{n}\text{, }&n\neq 0\\m=2\text{, }&n=0\end{matrix}\right,$$

Løs for n (complex solution)

$$n=\sqrt{m^{4}-4m^{3}-2m^{2}+8m+17}+m^{2}-2m-3$$

$$n=-\sqrt{m^{4}-4m^{3}-2m^{2}+8m+17}+m^{2}-2m-3$$

Løs for m

$$\left\{\begin{matrix}m=\frac{\sqrt{2n^{3}+16n^{2}-8n+4}}{2n}+1+\frac{1}{n}\text{; }m=-\frac{\sqrt{2n^{3}+16n^{2}-8n+4}}{2n}+1+\frac{1}{n}\text{, }&n\neq 0\text{ and }8n^{3}+64n^{2}-32n+16\geq 0\\m=2\text{, }&n=0\end{matrix}\right,$$

Løs for n

$$n=\sqrt{m^{4}-4m^{3}-2m^{2}+8m+17}+m^{2}-2m-3$$

$$n=-\sqrt{m^{4}-4m^{3}-2m^{2}+8m+17}+m^{2}-2m-3\text{, }m^{4}-4m^{3}-2m^{2}+8m+17\geq 0$$