Solve for P
\left\{\begin{matrix}P=\frac{nrt}{v}\text{, }&v\neq 0\\P\in \mathrm{R}\text{, }&\left(n=0\text{ or }r=0\text{ or }t=0\right)\text{ and }v=0\end{matrix}\right.
Solve for n
\left\{\begin{matrix}n=\frac{Pv}{rt}\text{, }&t\neq 0\text{ and }r\neq 0\\n\in \mathrm{R}\text{, }&\left(P=0\text{ and }t=0\right)\text{ or }\left(v=0\text{ and }t=0\right)\text{ or }\left(r=0\text{ and }v=0\text{ and }t\neq 0\right)\text{ or }\left(P=0\text{ and }r=0\text{ and }t\neq 0\right)\end{matrix}\right.
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vP=nrt
The equation is in standard form.
\frac{vP}{v}=\frac{nrt}{v}
Divide both sides by v.
P=\frac{nrt}{v}
Dividing by v undoes the multiplication by v.
nrt=Pv
Swap sides so that all variable terms are on the left hand side.
rtn=Pv
The equation is in standard form.
\frac{rtn}{rt}=\frac{Pv}{rt}
Divide both sides by rt.
n=\frac{Pv}{rt}
Dividing by rt undoes the multiplication by rt.
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