Solve for b (complex solution)
\left\{\begin{matrix}b=-\frac{r-a}{q}\text{, }&q\neq 0\\b\in \mathrm{C}\text{, }&a=r\text{ and }q=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-\frac{r-a}{q}\text{, }&q\neq 0\\b\in \mathrm{R}\text{, }&a=r\text{ and }q=0\end{matrix}\right.
Solve for a
a=bq+r
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bq+r=a
Swap sides so that all variable terms are on the left hand side.
bq=a-r
Subtract r from both sides.
qb=a-r
The equation is in standard form.
\frac{qb}{q}=\frac{a-r}{q}
Divide both sides by q.
b=\frac{a-r}{q}
Dividing by q undoes the multiplication by q.
bq+r=a
Swap sides so that all variable terms are on the left hand side.
bq=a-r
Subtract r from both sides.
qb=a-r
The equation is in standard form.
\frac{qb}{q}=\frac{a-r}{q}
Divide both sides by q.
b=\frac{a-r}{q}
Dividing by q undoes the multiplication by q.
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