Solve for L (complex solution)
\left\{\begin{matrix}L=-\frac{S}{r-1}\text{, }&r\neq 1\\L\in \mathrm{C}\text{, }&S=0\text{ and }r=1\end{matrix}\right.
Solve for L
\left\{\begin{matrix}L=-\frac{S}{r-1}\text{, }&r\neq 1\\L\in \mathrm{R}\text{, }&S=0\text{ and }r=1\end{matrix}\right.
Solve for S
S=L\left(1-r\right)
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S=L-Lr
Use the distributive property to multiply L by 1-r.
L-Lr=S
Swap sides so that all variable terms are on the left hand side.
\left(1-r\right)L=S
Combine all terms containing L.
\frac{\left(1-r\right)L}{1-r}=\frac{S}{1-r}
Divide both sides by 1-r.
L=\frac{S}{1-r}
Dividing by 1-r undoes the multiplication by 1-r.
S=L-Lr
Use the distributive property to multiply L by 1-r.
L-Lr=S
Swap sides so that all variable terms are on the left hand side.
\left(1-r\right)L=S
Combine all terms containing L.
\frac{\left(1-r\right)L}{1-r}=\frac{S}{1-r}
Divide both sides by 1-r.
L=\frac{S}{1-r}
Dividing by 1-r undoes the multiplication by 1-r.
S=L-Lr
Use the distributive property to multiply L by 1-r.
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