Solve {l}{3n-9m+2*2m-3mn=5}{o=5m-7n}{p=o}{q=p}{r=q}{text{Solvefor}stext{where}}{s=r}

$$\left. \begin{array} { l } { 3 n - 9 m + 2 \cdot 2 m - 3 m n = 5 }\\ { o = 5 m - 7 n }\\ { p = o }\\ { q = p }\\ { r = q }\\ { \text{Solve for } s \text{ where} } \\ { s = r } \end{array} \right.$$

Solve for n, m, o, p, q, r, s (complex solution)

$$r=s\text{, }s\in \mathrm{C}\text{, }n=\frac{-\sqrt{9s^{2}-300s-1700}-3s-20}{42}\text{, }m=\frac{-\sqrt{9s^{2}-300s-1700}+3s-20}{30}\text{, }o=s\text{, }p=s\text{, }q=s$$

$$r=s\text{, }s\in \mathrm{C}\text{, }n=\frac{5\left(\sqrt{9s^{2}-300s-1700}+3s+10\right)}{3\left(-\sqrt{9s^{2}-300s-1700}-3s+50\right)}\text{, }m=\frac{\sqrt{9s^{2}-300s-1700}+3s-20}{30}\text{, }o=s\text{, }p=s\text{, }q=s$$

Solve for n, m, o, p, q, r, s

$$r=s\text{, }s\in (-\infty,\frac{10(5-\sqrt{42})}{3}]\cup [\frac{10(\sqrt{42}+5)}{3},\infty)\text{, }n=\frac{-\sqrt{9s^{2}-300s-1700}-3s-20}{42}\text{, }m=\frac{-\sqrt{9s^{2}-300s-1700}+3s-20}{30}\text{, }o=s\text{, }p=s\text{, }q=s\text{; }r=s\text{, }s\in (-\infty,\frac{10(5-\sqrt{42})}{3}]\cup [\frac{10(\sqrt{42}+5)}{3},\infty)\text{, }n=\frac{5(\sqrt{9s^{2}-300s-1700}+3s+10)}{3(-\sqrt{9s^{2}-300s-1700}-3s+50)}\text{, }m=\frac{\sqrt{9s^{2}-300s-1700}+3s-20}{30}\text{, }o=s\text{, }p=s\text{, }q=s$$