Solve for f
\left\{\begin{matrix}f=g-\frac{T}{m}\text{, }&m\neq 0\\f\in \mathrm{R}\text{, }&T=0\text{ and }m=0\end{matrix}\right.
Solve for T
T=m\left(g-f\right)
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mg-mf=T
Swap sides so that all variable terms are on the left hand side.
-mf=T-mg
Subtract mg from both sides.
\left(-m\right)f=T-gm
The equation is in standard form.
\frac{\left(-m\right)f}{-m}=\frac{T-gm}{-m}
Divide both sides by -m.
f=\frac{T-gm}{-m}
Dividing by -m undoes the multiplication by -m.
f=g-\frac{T}{m}
Divide T-mg by -m.
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