Solve for Z
\left\{\begin{matrix}Z=\frac{ns}{cm}\text{, }&m\neq 0\text{ and }c\neq 0\text{ and }s\neq 0\\Z\in \mathrm{R}\text{, }&\left(m=0\text{ or }c=0\right)\text{ and }n=0\text{ and }s\neq 0\end{matrix}\right.
Solve for c
\left\{\begin{matrix}c=\frac{ns}{Zm}\text{, }&m\neq 0\text{ and }Z\neq 0\text{ and }s\neq 0\\c\in \mathrm{R}\text{, }&\left(m=0\text{ or }Z=0\right)\text{ and }n=0\text{ and }s\neq 0\end{matrix}\right.
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ns=Zcm
Multiply both sides of the equation by s.
Zcm=ns
Swap sides so that all variable terms are on the left hand side.
cmZ=ns
The equation is in standard form.
\frac{cmZ}{cm}=\frac{ns}{cm}
Divide both sides by cm.
Z=\frac{ns}{cm}
Dividing by cm undoes the multiplication by cm.
ns=Zcm
Multiply both sides of the equation by s.
Zcm=ns
Swap sides so that all variable terms are on the left hand side.
Zmc=ns
The equation is in standard form.
\frac{Zmc}{Zm}=\frac{ns}{Zm}
Divide both sides by Zm.
c=\frac{ns}{Zm}
Dividing by Zm undoes the multiplication by Zm.
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