Solve a=bq+r

$$a = b q + r$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{r-a}{q}\text{, }&q\neq 0\\b\in \mathrm{R}\text{, }&a=r\text{ and }q=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$bq+r=a$$

Subtract r from both sides.

$$bq=a-r$$

The equation is in standard form.

$$qb=a-r$$

Divide both sides by q.

$$\frac{qb}{q}=\frac{a-r}{q}$$

Dividing by q undoes the multiplication by q.

$$b=\frac{a-r}{q}$$

Solve for a

$$a=bq+r$$