Solve T=GMm/r^2quad{l}{G=10}{M=100}

$$T = G \frac { M m } { r ^ { 2 } } \quad \left. \begin{array} { l } { G = 10 } \\ { M = 100 } \end{array} \right.$$

Solve for G

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

Steps for Solving Linear Equation

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

$$Tr^{2}=GMm$$

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

$$GMm=Tr^{2}$$

The equation is in standard form.

$$MmG=Tr^{2}$$

Divide both sides by Mm.

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

Dividing by Mm undoes the multiplication by Mm.

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

Solve for M

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

Steps for Solving Linear Equation

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

$$Tr^{2}=GMm$$

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

$$GMm=Tr^{2}$$

The equation is in standard form.

$$GmM=Tr^{2}$$

Divide both sides by Gm.

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

Dividing by Gm undoes the multiplication by Gm.

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