Solve for F (complex solution)
\left\{\begin{matrix}F=\frac{Mr}{M_{a}S}\text{, }&M_{a}\neq 0\text{ and }S\neq 0\\F\in \mathrm{C}\text{, }&\left(r=0\text{ or }M=0\right)\text{ and }S=0\text{ and }M_{a}\neq 0\end{matrix}\right.
Solve for M (complex solution)
\left\{\begin{matrix}M=\frac{FM_{a}S}{r}\text{, }&r\neq 0\text{ and }M_{a}\neq 0\\M\in \mathrm{C}\text{, }&\left(S=0\text{ or }F=0\right)\text{ and }r=0\text{ and }M_{a}\neq 0\end{matrix}\right.
Solve for F
\left\{\begin{matrix}F=\frac{Mr}{M_{a}S}\text{, }&M_{a}\neq 0\text{ and }S\neq 0\\F\in \mathrm{R}\text{, }&\left(r=0\text{ or }M=0\right)\text{ and }S=0\text{ and }M_{a}\neq 0\end{matrix}\right.
Solve for M
\left\{\begin{matrix}M=\frac{FM_{a}S}{r}\text{, }&r\neq 0\text{ and }M_{a}\neq 0\\M\in \mathrm{R}\text{, }&\left(S=0\text{ or }F=0\right)\text{ and }r=0\text{ and }M_{a}\neq 0\end{matrix}\right.
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FSM_{a}=Mr
Multiply both sides of the equation by M_{a}.
M_{a}SF=Mr
The equation is in standard form.
\frac{M_{a}SF}{M_{a}S}=\frac{Mr}{M_{a}S}
Divide both sides by SM_{a}.
F=\frac{Mr}{M_{a}S}
Dividing by SM_{a} undoes the multiplication by SM_{a}.
FSM_{a}=Mr
Multiply both sides of the equation by M_{a}.
Mr=FSM_{a}
Swap sides so that all variable terms are on the left hand side.
rM=FM_{a}S
The equation is in standard form.
\frac{rM}{r}=\frac{FM_{a}S}{r}
Divide both sides by r.
M=\frac{FM_{a}S}{r}
Dividing by r undoes the multiplication by r.
FSM_{a}=Mr
Multiply both sides of the equation by M_{a}.
M_{a}SF=Mr
The equation is in standard form.
\frac{M_{a}SF}{M_{a}S}=\frac{Mr}{M_{a}S}
Divide both sides by SM_{a}.
F=\frac{Mr}{M_{a}S}
Dividing by SM_{a} undoes the multiplication by SM_{a}.
FSM_{a}=Mr
Multiply both sides of the equation by M_{a}.
Mr=FSM_{a}
Swap sides so that all variable terms are on the left hand side.
rM=FM_{a}S
The equation is in standard form.
\frac{rM}{r}=\frac{FM_{a}S}{r}
Divide both sides by r.
M=\frac{FM_{a}S}{r}
Dividing by r undoes the multiplication by r.
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