Solve for a
\left\{\begin{matrix}a=\frac{r}{2t+b}\text{, }&b\neq -2t\\a\in \mathrm{R}\text{, }&r=0\text{ and }b=-2t\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-2t+\frac{r}{a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&r=0\text{ and }a=0\end{matrix}\right.
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r=ab+2at
Use the distributive property to multiply a by b+2t.
ab+2at=r
Swap sides so that all variable terms are on the left hand side.
\left(b+2t\right)a=r
Combine all terms containing a.
\left(2t+b\right)a=r
The equation is in standard form.
\frac{\left(2t+b\right)a}{2t+b}=\frac{r}{2t+b}
Divide both sides by b+2t.
a=\frac{r}{2t+b}
Dividing by b+2t undoes the multiplication by b+2t.
r=ab+2at
Use the distributive property to multiply a by b+2t.
ab+2at=r
Swap sides so that all variable terms are on the left hand side.
ab=r-2at
Subtract 2at from both sides.
\frac{ab}{a}=\frac{r-2at}{a}
Divide both sides by a.
b=\frac{r-2at}{a}
Dividing by a undoes the multiplication by a.
b=-2t+\frac{r}{a}
Divide r-2ta by a.
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