Solve for B (complex solution)
\left\{\begin{matrix}B=-\frac{P-A}{PT}\text{, }&T\neq 0\text{ and }P\neq 0\\B\in \mathrm{C}\text{, }&\left(A=P\text{ and }T=0\right)\text{ or }\left(A=0\text{ and }P=0\text{ and }T\neq 0\right)\end{matrix}\right.
Solve for B
\left\{\begin{matrix}B=-\frac{P-A}{PT}\text{, }&T\neq 0\text{ and }P\neq 0\\B\in \mathrm{R}\text{, }&\left(A=P\text{ and }T=0\right)\text{ or }\left(A=0\text{ and }P=0\text{ and }T\neq 0\right)\end{matrix}\right.
Solve for A
A=P\left(BT+1\right)
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P+PBT=A
Swap sides so that all variable terms are on the left hand side.
PBT=A-P
Subtract P from both sides.
PTB=A-P
The equation is in standard form.
\frac{PTB}{PT}=\frac{A-P}{PT}
Divide both sides by PT.
B=\frac{A-P}{PT}
Dividing by PT undoes the multiplication by PT.
P+PBT=A
Swap sides so that all variable terms are on the left hand side.
PBT=A-P
Subtract P from both sides.
PTB=A-P
The equation is in standard form.
\frac{PTB}{PT}=\frac{A-P}{PT}
Divide both sides by PT.
B=\frac{A-P}{PT}
Dividing by PT undoes the multiplication by PT.
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