Solve for P (complex solution)
\left\{\begin{matrix}P=\frac{RTn}{V}\text{, }&V\neq 0\\P\in \mathrm{C}\text{, }&\left(n=0\text{ or }R=0\text{ or }T=0\right)\text{ and }V=0\end{matrix}\right.
Solve for R (complex solution)
\left\{\begin{matrix}R=\frac{PV}{Tn}\text{, }&T\neq 0\text{ and }n\neq 0\\R\in \mathrm{C}\text{, }&\left(P=0\text{ and }T=0\right)\text{ or }\left(V=0\text{ and }T=0\right)\text{ or }\left(V=0\text{ and }n=0\text{ and }T\neq 0\right)\text{ or }\left(P=0\text{ and }n=0\text{ and }T\neq 0\right)\end{matrix}\right.
Solve for P
\left\{\begin{matrix}P=\frac{RTn}{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 R
\left\{\begin{matrix}R=\frac{PV}{Tn}\text{, }&T\neq 0\text{ and }n\neq 0\\R\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(V=0\text{ and }n=0\text{ and }T\neq 0\right)\text{ or }\left(P=0\text{ and }n=0\text{ and }T\neq 0\right)\end{matrix}\right.
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VP=RTn
The equation is in standard form.
\frac{VP}{V}=\frac{RTn}{V}
Divide both sides by V.
P=\frac{RTn}{V}
Dividing by V undoes the multiplication by V.
nRT=PV
Swap sides so that all variable terms are on the left hand side.
TnR=PV
The equation is in standard form.
\frac{TnR}{Tn}=\frac{PV}{Tn}
Divide both sides by nT.
R=\frac{PV}{Tn}
Dividing by nT undoes the multiplication by nT.
VP=RTn
The equation is in standard form.
\frac{VP}{V}=\frac{RTn}{V}
Divide both sides by V.
P=\frac{RTn}{V}
Dividing by V undoes the multiplication by V.
nRT=PV
Swap sides so that all variable terms are on the left hand side.
TnR=PV
The equation is in standard form.
\frac{TnR}{Tn}=\frac{PV}{Tn}
Divide both sides by nT.
R=\frac{PV}{Tn}
Dividing by nT undoes the multiplication by nT.
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