Solve 4ab-cd=e

$$4 a b - c d = e$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{cd+e}{4b}\text{, }&b\neq 0\\a\in \mathrm{C}\text{, }&c=-\frac{e}{d}\text{ and }d\neq 0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add cd to both sides.

$$4ab=e+cd$$

The equation is in standard form.

$$4ba=cd+e$$

Divide both sides by 4b.

$$\frac{4ba}{4b}=\frac{cd+e}{4b}$$

Dividing by 4b undoes the multiplication by 4b.

$$a=\frac{cd+e}{4b}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{cd+e}{4a}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&c=-\frac{e}{d}\text{ and }d\neq 0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add cd to both sides.

$$4ab=e+cd$$

The equation is in standard form.

$$4ab=cd+e$$

Divide both sides by 4a.

$$\frac{4ab}{4a}=\frac{cd+e}{4a}$$

Dividing by 4a undoes the multiplication by 4a.

$$b=\frac{cd+e}{4a}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{cd+e}{4b}\text{, }&b\neq 0\\a\in \mathrm{R}\text{, }&c=-\frac{e}{d}\text{ and }d\neq 0\text{ and }b=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add cd to both sides.

$$4ab=e+cd$$

The equation is in standard form.

$$4ba=cd+e$$

Divide both sides by 4b.

$$\frac{4ba}{4b}=\frac{cd+e}{4b}$$

Dividing by 4b undoes the multiplication by 4b.

$$a=\frac{cd+e}{4b}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{cd+e}{4a}\text{, }&a\neq 0\\b\in \mathrm{R}\text{, }&c=-\frac{e}{d}\text{ and }d\neq 0\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add cd to both sides.

$$4ab=e+cd$$

The equation is in standard form.

$$4ab=cd+e$$

Divide both sides by 4a.

$$\frac{4ab}{4a}=\frac{cd+e}{4a}$$

Dividing by 4a undoes the multiplication by 4a.

$$b=\frac{cd+e}{4a}$$