Solve dW=GMm/r^2dr

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

Solve for G (complex solution)

$$\left\{\begin{matrix}G=\frac{Wr}{Mm}\text{, }&m\neq 0\text{ and }M\neq 0\text{ and }r\neq 0\\G\in \mathrm{C}\text{, }&\left(d=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }m=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }M=0\text{ and }m\neq 0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$dWr^{2}=GMmdr$$

Swap sides so that all variable terms are on the left hand side.

$$GMmdr=dWr^{2}$$

The equation is in standard form.

$$MdmrG=Wdr^{2}$$

Divide both sides by Mmdr.

$$\frac{MdmrG}{Mdmr}=\frac{Wdr^{2}}{Mdmr}$$

Dividing by Mmdr undoes the multiplication by Mmdr.

$$G=\frac{Wdr^{2}}{Mdmr}$$

Divide dWr^{2} by Mmdr.

$$G=\frac{Wr}{Mm}$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=\frac{Wr}{Gm}\text{, }&m\neq 0\text{ and }G\neq 0\text{ and }r\neq 0\\M\in \mathrm{C}\text{, }&\left(d=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }m=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }G=0\text{ and }m\neq 0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$dWr^{2}=GMmdr$$

Swap sides so that all variable terms are on the left hand side.

$$GMmdr=dWr^{2}$$

The equation is in standard form.

$$GdmrM=Wdr^{2}$$

Divide both sides by Gmdr.

$$\frac{GdmrM}{Gdmr}=\frac{Wdr^{2}}{Gdmr}$$

Dividing by Gmdr undoes the multiplication by Gmdr.

$$M=\frac{Wdr^{2}}{Gdmr}$$

Divide dWr^{2} by Gmdr.

$$M=\frac{Wr}{Gm}$$

Solve for G

$$\left\{\begin{matrix}G=\frac{Wr}{Mm}\text{, }&m\neq 0\text{ and }M\neq 0\text{ and }r\neq 0\\G\in \mathrm{R}\text{, }&\left(d=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }m=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }M=0\text{ and }m\neq 0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$dWr^{2}=GMmdr$$

Swap sides so that all variable terms are on the left hand side.

$$GMmdr=dWr^{2}$$

The equation is in standard form.

$$MdmrG=Wdr^{2}$$

Divide both sides by Mmdr.

$$\frac{MdmrG}{Mdmr}=\frac{Wdr^{2}}{Mdmr}$$

Dividing by Mmdr undoes the multiplication by Mmdr.

$$G=\frac{Wdr^{2}}{Mdmr}$$

Divide dWr^{2} by Mmdr.

$$G=\frac{Wr}{Mm}$$

Solve for M

$$\left\{\begin{matrix}M=\frac{Wr}{Gm}\text{, }&m\neq 0\text{ and }G\neq 0\text{ and }r\neq 0\\M\in \mathrm{R}\text{, }&\left(d=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }m=0\text{ and }r\neq 0\right)\text{ or }\left(W=0\text{ and }G=0\text{ and }m\neq 0\text{ and }r\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$dWr^{2}=GMmdr$$

Swap sides so that all variable terms are on the left hand side.

$$GMmdr=dWr^{2}$$

The equation is in standard form.

$$GdmrM=Wdr^{2}$$

Divide both sides by Gmdr.

$$\frac{GdmrM}{Gdmr}=\frac{Wdr^{2}}{Gdmr}$$

Dividing by Gmdr undoes the multiplication by Gmdr.

$$M=\frac{Wdr^{2}}{Gdmr}$$

Divide dWr^{2} by Gmdr.

$$M=\frac{Wr}{Gm}$$