Solve for N (complex solution)
\left\{\begin{matrix}N=\frac{muv}{eFR}\text{, }&F\neq 0\text{ and }R\neq 0\\N\in \mathrm{C}\text{, }&\left(v=0\text{ or }m=0\text{ or }u=0\right)\text{ and }R=0\text{ and }F\neq 0\end{matrix}\right.
Solve for F
\left\{\begin{matrix}F=\frac{muv}{eNR}\text{, }&v\neq 0\text{ and }m\neq 0\text{ and }u\neq 0\text{ and }N\neq 0\text{ and }R\neq 0\\F\neq 0\text{, }&\left(R=0\text{ and }m=0\right)\text{ or }\left(R=0\text{ and }v=0\right)\text{ or }\left(N=0\text{ and }m=0\right)\text{ or }\left(N=0\text{ and }v=0\right)\text{ or }\left(N=0\text{ and }u=0\text{ and }v\neq 0\text{ and }m\neq 0\right)\text{ or }\left(R=0\text{ and }u=0\text{ and }v\neq 0\text{ and }m\neq 0\right)\end{matrix}\right.
Solve for N
\left\{\begin{matrix}N=\frac{muv}{eFR}\text{, }&F\neq 0\text{ and }R\neq 0\\N\in \mathrm{R}\text{, }&\left(v=0\text{ or }m=0\text{ or }u=0\right)\text{ and }R=0\text{ and }F\neq 0\end{matrix}\right.
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umv=RNeF
Multiply both sides of the equation by F.
RNeF=umv
Swap sides so that all variable terms are on the left hand side.
eFRN=muv
The equation is in standard form.
\frac{eFRN}{eFR}=\frac{muv}{eFR}
Divide both sides by ReF.
N=\frac{muv}{eFR}
Dividing by ReF undoes the multiplication by ReF.
umv=RNeF
Variable F cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by F.
RNeF=umv
Swap sides so that all variable terms are on the left hand side.
eNRF=muv
The equation is in standard form.
\frac{eNRF}{eNR}=\frac{muv}{eNR}
Divide both sides by RNe.
F=\frac{muv}{eNR}
Dividing by RNe undoes the multiplication by RNe.
F=\frac{muv}{eNR}\text{, }F\neq 0
Variable F cannot be equal to 0.
umv=RNeF
Multiply both sides of the equation by F.
RNeF=umv
Swap sides so that all variable terms are on the left hand side.
eFRN=muv
The equation is in standard form.
\frac{eFRN}{eFR}=\frac{muv}{eFR}
Divide both sides by ReF.
N=\frac{muv}{eFR}
Dividing by ReF undoes the multiplication by ReF.
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