Solve for g
\left\{\begin{matrix}g=\frac{T}{r+tu}\text{, }&r\neq -tu\\g\in \mathrm{R}\text{, }&T=0\text{ and }r=-tu\end{matrix}\right.
Solve for T
T=g\left(r+tu\right)
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gr+gut=T
Swap sides so that all variable terms are on the left hand side.
\left(r+ut\right)g=T
Combine all terms containing g.
\left(r+tu\right)g=T
The equation is in standard form.
\frac{\left(r+tu\right)g}{r+tu}=\frac{T}{r+tu}
Divide both sides by r+ut.
g=\frac{T}{r+tu}
Dividing by r+ut undoes the multiplication by r+ut.
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