Solve for R (complex solution)
\left\{\begin{matrix}R=\frac{Mpv}{Tx}\text{, }&T\neq 0\text{ and }x\neq 0\text{ and }M\neq 0\\R\in \mathrm{C}\text{, }&\left(v=0\text{ and }T=0\text{ and }M\neq 0\right)\text{ or }\left(p=0\text{ and }T=0\text{ and }M\neq 0\right)\text{ or }\left(p=0\text{ and }x=0\text{ and }T\neq 0\text{ and }M\neq 0\right)\text{ or }\left(v=0\text{ and }x=0\text{ and }T\neq 0\text{ and }M\neq 0\right)\end{matrix}\right.
Solve for M
\left\{\begin{matrix}M=\frac{RTx}{pv}\text{, }&T\neq 0\text{ and }R\neq 0\text{ and }x\neq 0\text{ and }v\neq 0\text{ and }p\neq 0\\M\neq 0\text{, }&\left(p=0\text{ and }R=0\right)\text{ or }\left(p=0\text{ and }T=0\right)\text{ or }\left(v=0\text{ and }R=0\right)\text{ or }\left(v=0\text{ and }T=0\right)\text{ or }\left(v=0\text{ and }x=0\text{ and }T\neq 0\text{ and }R\neq 0\right)\text{ or }\left(p=0\text{ and }x=0\text{ and }T\neq 0\text{ and }R\neq 0\right)\end{matrix}\right.
Solve for R
\left\{\begin{matrix}R=\frac{Mpv}{Tx}\text{, }&T\neq 0\text{ and }x\neq 0\text{ and }M\neq 0\\R\in \mathrm{R}\text{, }&\left(v=0\text{ and }T=0\text{ and }M\neq 0\right)\text{ or }\left(p=0\text{ and }T=0\text{ and }M\neq 0\right)\text{ or }\left(p=0\text{ and }x=0\text{ and }T\neq 0\text{ and }M\neq 0\right)\text{ or }\left(v=0\text{ and }x=0\text{ and }T\neq 0\text{ and }M\neq 0\right)\end{matrix}\right.
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pvM=xRT
Multiply both sides of the equation by M.
xRT=pvM
Swap sides so that all variable terms are on the left hand side.
TxR=Mpv
The equation is in standard form.
\frac{TxR}{Tx}=\frac{Mpv}{Tx}
Divide both sides by xT.
R=\frac{Mpv}{Tx}
Dividing by xT undoes the multiplication by xT.
pvM=xRT
Variable M cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by M.
pvM=RTx
The equation is in standard form.
\frac{pvM}{pv}=\frac{RTx}{pv}
Divide both sides by pv.
M=\frac{RTx}{pv}
Dividing by pv undoes the multiplication by pv.
M=\frac{RTx}{pv}\text{, }M\neq 0
Variable M cannot be equal to 0.
pvM=xRT
Multiply both sides of the equation by M.
xRT=pvM
Swap sides so that all variable terms are on the left hand side.
TxR=Mpv
The equation is in standard form.
\frac{TxR}{Tx}=\frac{Mpv}{Tx}
Divide both sides by xT.
R=\frac{Mpv}{Tx}
Dividing by xT undoes the multiplication by xT.
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