Solve ax-ab=c

$$a x - a b = c$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Combine all terms containing a.

$$\left(x-b\right)a=c$$

Divide both sides by x-b.

$$\frac{\left(x-b\right)a}{x-b}=\frac{c}{x-b}$$

Dividing by x-b undoes the multiplication by x-b.

$$a=\frac{c}{x-b}$$

Solve for b (complex solution)

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-ab=c-ax$$

The equation is in standard form.

$$\left(-a\right)b=c-ax$$

Divide both sides by -a.

$$\frac{\left(-a\right)b}{-a}=\frac{c-ax}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$b=\frac{c-ax}{-a}$$

Divide c-ax by -a.

$$b=x-\frac{c}{a}$$

Solve for a

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

Steps for Solving Linear Equation

Combine all terms containing a.

$$\left(x-b\right)a=c$$

Divide both sides by x-b.

$$\frac{\left(x-b\right)a}{x-b}=\frac{c}{x-b}$$

Dividing by x-b undoes the multiplication by x-b.

$$a=\frac{c}{x-b}$$

Solve for b

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

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-ab=c-ax$$

The equation is in standard form.

$$\left(-a\right)b=c-ax$$

Divide both sides by -a.

$$\frac{\left(-a\right)b}{-a}=\frac{c-ax}{-a}$$

Dividing by -a undoes the multiplication by -a.

$$b=\frac{c-ax}{-a}$$

Divide c-ax by -a.

$$b=x-\frac{c}{a}$$