Solve for b
\left\{\begin{matrix}b=-\frac{c-a}{ct}\text{, }&c\neq 0\text{ and }t\neq 0\\b\in \mathrm{R}\text{, }&\left(a=0\text{ and }c=0\right)\text{ or }\left(a=c\text{ and }t=0\text{ and }c\neq 0\right)\end{matrix}\right.
Solve for a
a=c\left(bt+1\right)
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a=c+cbt
Use the distributive property to multiply c by 1+bt.
c+cbt=a
Swap sides so that all variable terms are on the left hand side.
cbt=a-c
Subtract c from both sides.
ctb=a-c
The equation is in standard form.
\frac{ctb}{ct}=\frac{a-c}{ct}
Divide both sides by ct.
b=\frac{a-c}{ct}
Dividing by ct undoes the multiplication by ct.
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