Solve for O
\left\{\begin{matrix}O=-\frac{at-V}{v}\text{, }&v\neq 0\\O\in \mathrm{R}\text{, }&V=at\text{ and }v=0\end{matrix}\right.
Solve for V
V=at+Ov
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vO+at=V
Swap sides so that all variable terms are on the left hand side.
vO=V-at
Subtract at from both sides.
\frac{vO}{v}=\frac{V-at}{v}
Divide both sides by v.
O=\frac{V-at}{v}
Dividing by v undoes the multiplication by v.
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