Solve F=Gmm/r^2

$$F = \frac { G m m } { r ^ { 2 } }$$

Solve for G

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

Steps for Solving Linear Equation

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

$$Fr^{2}=Gmm$$

Multiply m and m to get m^{2}.

$$Fr^{2}=Gm^{2}$$

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

$$Gm^{2}=Fr^{2}$$

The equation is in standard form.

$$m^{2}G=Fr^{2}$$

Divide both sides by m^{2}.

$$\frac{m^{2}G}{m^{2}}=\frac{Fr^{2}}{m^{2}}$$

Dividing by m^{2} undoes the multiplication by m^{2}.

$$G=\frac{Fr^{2}}{m^{2}}$$

Solve for F

$$F=\left(\frac{m}{r}\right)^{2}G$$

$$r\neq 0$$