Solve for a
\left\{\begin{matrix}a=\frac{Fcg}{m}\text{, }&m\neq 0\text{ and }g\neq 0\text{ and }c\neq 0\\a\in \mathrm{R}\text{, }&F=0\text{ and }m=0\text{ and }g\neq 0\text{ and }c\neq 0\end{matrix}\right.
Solve for F
F=\frac{am}{cg}
c\neq 0\text{ and }g\neq 0
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Fcg=ma
Multiply both sides of the equation by cg.
ma=Fcg
Swap sides so that all variable terms are on the left hand side.
\frac{ma}{m}=\frac{Fcg}{m}
Divide both sides by m.
a=\frac{Fcg}{m}
Dividing by m undoes the multiplication by m.
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