Solve GMm/r^2=mg

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

Solve for G (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$GMm=mgr^{2}$$

Reorder the terms.

$$GMm=gmr^{2}$$

The equation is in standard form.

$$MmG=gmr^{2}$$

Divide both sides by Mm.

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

Dividing by Mm undoes the multiplication by Mm.

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

Divide gmr^{2} by Mm.

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

Solve for M (complex solution)

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

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$GMm=mgr^{2}$$

Reorder the terms.

$$GMm=gmr^{2}$$

The equation is in standard form.

$$GmM=gmr^{2}$$

Divide both sides by Gm.

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

Dividing by Gm undoes the multiplication by Gm.

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

Divide gmr^{2} by Gm.

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

Solve for G

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

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$GMm=mgr^{2}$$

Reorder the terms.

$$GMm=gmr^{2}$$

The equation is in standard form.

$$MmG=gmr^{2}$$

Divide both sides by Mm.

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

Dividing by Mm undoes the multiplication by Mm.

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

Divide gmr^{2} by Mm.

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

Solve for M

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

Steps for Solving Linear Equation

Multiply both sides of the equation by r^{2}.

$$GMm=mgr^{2}$$

Reorder the terms.

$$GMm=gmr^{2}$$

The equation is in standard form.

$$GmM=gmr^{2}$$

Divide both sides by Gm.

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

Dividing by Gm undoes the multiplication by Gm.

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

Divide gmr^{2} by Gm.

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