Solve x=bq+r

$$x = b q + r$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

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

$$bq+r=x$$

Subtract r from both sides.

$$bq=x-r$$

The equation is in standard form.

$$qb=x-r$$

Divide both sides by q.

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

Dividing by q undoes the multiplication by q.

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

Solve for q (complex solution)

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

Steps for Solving Linear Equation

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

$$bq+r=x$$

Subtract r from both sides.

$$bq=x-r$$

Divide both sides by b.

$$\frac{bq}{b}=\frac{x-r}{b}$$

Dividing by b undoes the multiplication by b.

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

Solve for b

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

Steps for Solving Linear Equation

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

$$bq+r=x$$

Subtract r from both sides.

$$bq=x-r$$

The equation is in standard form.

$$qb=x-r$$

Divide both sides by q.

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

Dividing by q undoes the multiplication by q.

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

Solve for q

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

Steps for Solving Linear Equation

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

$$bq+r=x$$

Subtract r from both sides.

$$bq=x-r$$

Divide both sides by b.

$$\frac{bq}{b}=\frac{x-r}{b}$$

Dividing by b undoes the multiplication by b.

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