Solve r=3m^2-5/n

$$r = \frac { 3 m ^ { 2 } - 5 } { n }$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{5-3m^{2}}{r}\text{, }&m\neq -\frac{\sqrt{15}}{3}\text{ and }m\neq \frac{\sqrt{15}}{3}\text{ and }r\neq 0\\n\neq 0\text{, }&\left(m=\frac{\sqrt{15}}{3}\text{ or }m=-\frac{\sqrt{15}}{3}\right)\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$rn=3m^{2}-5$$

Divide both sides by r.

$$\frac{rn}{r}=\frac{3m^{2}-5}{r}$$

Dividing by r undoes the multiplication by r.

$$n=\frac{3m^{2}-5}{r}$$

Variable n cannot be equal to 0.

$$n=\frac{3m^{2}-5}{r}\text{, }n\neq 0$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{5-3m^{2}}{r}\text{, }&r\neq 0\text{ and }|m|\neq \frac{\sqrt{15}}{3}\\n\neq 0\text{, }&r=0\text{ and }|m|=\frac{\sqrt{15}}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$rn=3m^{2}-5$$

Divide both sides by r.

$$\frac{rn}{r}=\frac{3m^{2}-5}{r}$$

Dividing by r undoes the multiplication by r.

$$n=\frac{3m^{2}-5}{r}$$

Variable n cannot be equal to 0.

$$n=\frac{3m^{2}-5}{r}\text{, }n\neq 0$$

Solve for m (complex solution)

$$m=-\frac{\sqrt{3\left(nr+5\right)}}{3}$$

$$m=\frac{\sqrt{3\left(nr+5\right)}}{3}\text{, }n\neq 0$$

Solve for m

$$m=\frac{\sqrt{3\left(nr+5\right)}}{3}$$

$$m=-\frac{\sqrt{3\left(nr+5\right)}}{3}\text{, }\left(n>0\text{ or }r\leq -\frac{5}{n}\right)\text{ and }\left(n<0\text{ or }r\geq -\frac{5}{n}\right)\text{ and }n\neq 0$$