Solve for C (complex solution)
\left\{\begin{matrix}C=\frac{2FS}{P}-3\text{, }&P\neq 0\\C\in \mathrm{C}\text{, }&\left(F=0\text{ or }S=0\right)\text{ and }P=0\end{matrix}\right.
Solve for F (complex solution)
\left\{\begin{matrix}F=\frac{P\left(C+3\right)}{2S}\text{, }&S\neq 0\\F\in \mathrm{C}\text{, }&\left(P=0\text{ or }C=-3\right)\text{ and }S=0\end{matrix}\right.
Solve for C
\left\{\begin{matrix}C=\frac{2FS}{P}-3\text{, }&P\neq 0\\C\in \mathrm{R}\text{, }&\left(F=0\text{ or }S=0\right)\text{ and }P=0\end{matrix}\right.
Solve for F
\left\{\begin{matrix}F=\frac{P\left(C+3\right)}{2S}\text{, }&S\neq 0\\F\in \mathrm{R}\text{, }&\left(P=0\text{ or }C=-3\right)\text{ and }S=0\end{matrix}\right.
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2SF-CP=3P
Swap sides so that all variable terms are on the left hand side.
-CP=3P-2SF
Subtract 2SF from both sides.
\left(-P\right)C=3P-2FS
The equation is in standard form.
\frac{\left(-P\right)C}{-P}=\frac{3P-2FS}{-P}
Divide both sides by -P.
C=\frac{3P-2FS}{-P}
Dividing by -P undoes the multiplication by -P.
C=\frac{2FS}{P}-3
Divide -2FS+3P by -P.
2SF-CP=3P
Swap sides so that all variable terms are on the left hand side.
2SF=3P+CP
Add CP to both sides.
2SF=CP+3P
The equation is in standard form.
\frac{2SF}{2S}=\frac{P\left(C+3\right)}{2S}
Divide both sides by 2S.
F=\frac{P\left(C+3\right)}{2S}
Dividing by 2S undoes the multiplication by 2S.
2SF-CP=3P
Swap sides so that all variable terms are on the left hand side.
-CP=3P-2SF
Subtract 2SF from both sides.
\left(-P\right)C=3P-2FS
The equation is in standard form.
\frac{\left(-P\right)C}{-P}=\frac{3P-2FS}{-P}
Divide both sides by -P.
C=\frac{3P-2FS}{-P}
Dividing by -P undoes the multiplication by -P.
C=\frac{2FS}{P}-3
Divide -2FS+3P by -P.
2SF-CP=3P
Swap sides so that all variable terms are on the left hand side.
2SF=3P+CP
Add CP to both sides.
2SF=CP+3P
The equation is in standard form.
\frac{2SF}{2S}=\frac{P\left(C+3\right)}{2S}
Divide both sides by 2S.
F=\frac{P\left(C+3\right)}{2S}
Dividing by 2S undoes the multiplication by 2S.
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