Solve for A
\left\{\begin{matrix}A=0\text{, }&S\neq 0\\A\in \mathrm{R}\text{, }&D=\frac{BI}{S}\text{ and }S\neq 0\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=\frac{DS}{I}\text{, }&I\neq 0\text{ and }S\neq 0\\B\in \mathrm{R}\text{, }&\left(A=0\text{ and }S\neq 0\right)\text{ or }\left(D=0\text{ and }I=0\text{ and }S\neq 0\right)\end{matrix}\right.
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IAB=ADS
Multiply both sides of the equation by S.
IAB-ADS=0
Subtract ADS from both sides.
ABI-ADS=0
Reorder the terms.
\left(BI-DS\right)A=0
Combine all terms containing A.
A=0
Divide 0 by IB-SD.
IAB=ADS
Multiply both sides of the equation by S.
AIB=ADS
The equation is in standard form.
\frac{AIB}{AI}=\frac{ADS}{AI}
Divide both sides by IA.
B=\frac{ADS}{AI}
Dividing by IA undoes the multiplication by IA.
B=\frac{DS}{I}
Divide ADS by IA.
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