Solve GmM/r^2=mV^2/r

$$G \frac { m M } { r ^ { 2 } } = m \frac { V ^ { 2 } } { r }$$

Solve for G

$$\left\{\begin{matrix}G=\frac{rV^{2}}{M}\text{, }&M\neq 0\text{ and }r\neq 0\\G\in \mathrm{R}\text{, }&\left(m=0\text{ and }r\neq 0\right)\text{ or }\left(V=0\text{ and }M=0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}, the least common multiple of r^{2},r.

$$GmM=mrV^{2}$$

Reorder the terms.

$$GMm=mrV^{2}$$

The equation is in standard form.

$$MmG=mrV^{2}$$

Divide both sides by Mm.

$$\frac{MmG}{Mm}=\frac{mrV^{2}}{Mm}$$

Dividing by Mm undoes the multiplication by Mm.

$$G=\frac{mrV^{2}}{Mm}$$

Divide mrV^{2} by Mm.

$$G=\frac{rV^{2}}{M}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{rV^{2}}{G}\text{, }&G\neq 0\text{ and }r\neq 0\\M\in \mathrm{R}\text{, }&\left(m=0\text{ and }r\neq 0\right)\text{ or }\left(V=0\text{ and }G=0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}, the least common multiple of r^{2},r.

$$GmM=mrV^{2}$$

Divide both sides by Gm.

$$\frac{GmM}{Gm}=\frac{mrV^{2}}{Gm}$$

Dividing by Gm undoes the multiplication by Gm.

$$M=\frac{mrV^{2}}{Gm}$$

Divide mrV^{2} by Gm.

$$M=\frac{rV^{2}}{G}$$