Solve ax-b=cx+d

$$a x - b = c x + d$$

Solve for a (complex solution)

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

Steps for Solving Linear Equation

Add b to both sides.

$$ax=cx+d+b$$

The equation is in standard form.

$$xa=cx+b+d$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{cx+b+d}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{cx+b+d}{x}$$

Solve for a

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

Steps for Solving Linear Equation

Add b to both sides.

$$ax=cx+d+b$$

The equation is in standard form.

$$xa=cx+b+d$$

Divide both sides by x.

$$\frac{xa}{x}=\frac{cx+b+d}{x}$$

Dividing by x undoes the multiplication by x.

$$a=\frac{cx+b+d}{x}$$

Solve for b

$$b=ax-cx-d$$

Steps for Solving Linear Equation

Subtract ax from both sides.

$$-b=cx+d-ax$$

The equation is in standard form.

$$-b=cx-ax+d$$

Divide both sides by -1.

$$\frac{-b}{-1}=\frac{cx-ax+d}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$b=\frac{cx-ax+d}{-1}$$

Divide cx+d-ax by -1.

$$b=-\left(cx-ax+d\right)$$