Solve for m
\left\{\begin{matrix}m=\frac{S-n}{nw}\text{, }&w\neq 0\text{ and }n\neq 0\\m\in \mathrm{R}\text{, }&\left(n=0\text{ and }S=0\right)\text{ or }\left(n=S\text{ and }w=0\right)\end{matrix}\right.
Solve for S
S=n\left(mw+1\right)
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S-mnw=n
Swap sides so that all variable terms are on the left hand side.
-mnw=n-S
Subtract S from both sides.
\left(-nw\right)m=n-S
The equation is in standard form.
\frac{\left(-nw\right)m}{-nw}=\frac{n-S}{-nw}
Divide both sides by -nw.
m=\frac{n-S}{-nw}
Dividing by -nw undoes the multiplication by -nw.
m=-\frac{n-S}{nw}
Divide n-S by -nw.
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