Solve for c
\left\{\begin{matrix}c=-m\sin(mtw)+\frac{A}{v}\text{, }&v\neq 0\\c\in \mathrm{R}\text{, }&A=0\text{ and }v=0\end{matrix}\right.
Solve for A
A=v\left(m\sin(mtw)+c\right)
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vc+vm\sin(wmt)=A
Swap sides so that all variable terms are on the left hand side.
vc=A-vm\sin(wmt)
Subtract vm\sin(wmt) from both sides.
vc=-mv\sin(mtw)+A
The equation is in standard form.
\frac{vc}{v}=\frac{-mv\sin(mtw)+A}{v}
Divide both sides by v.
c=\frac{-mv\sin(mtw)+A}{v}
Dividing by v undoes the multiplication by v.
c=-m\sin(mtw)+\frac{A}{v}
Divide A-vm\sin(wmt) by v.
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