Solve F=-GMm/r^2

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

Solve for G

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

Steps for Solving Linear Equation

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

$$Fr^{2}=\left(-G\right)Mm$$

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

$$\left(-G\right)Mm=Fr^{2}$$

Reorder the terms.

$$-GMm=Fr^{2}$$

The equation is in standard form.

$$\left(-Mm\right)G=Fr^{2}$$

Divide both sides by -Mm.

$$\frac{\left(-Mm\right)G}{-Mm}=\frac{Fr^{2}}{-Mm}$$

Dividing by -Mm undoes the multiplication by -Mm.

$$G=\frac{Fr^{2}}{-Mm}$$

Divide Fr^{2} by -Mm.

$$G=-\frac{Fr^{2}}{Mm}$$

Solve for F

$$F=-\frac{GMm}{r^{2}}$$

$$r\neq 0$$