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.
Solve for F
F=\frac{GMm}{r^{2}}
r\neq 0
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Fr^{2}=GmM
Multiply both sides of the equation by r^{2}.
GmM=Fr^{2}
Swap sides so that all variable terms are on the left hand side.
MmG=Fr^{2}
The equation is in standard form.
\frac{MmG}{Mm}=\frac{Fr^{2}}{Mm}
Divide both sides by mM.
G=\frac{Fr^{2}}{Mm}
Dividing by mM undoes the multiplication by mM.
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