Solve a=varepsilon+xvarepsilon+cx

$$a = \varepsilon + x \varepsilon + c x$$

Solve for c (complex solution)

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

Steps for Solving Linear Equation

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

$$\epsilon +x\epsilon +cx=a$$

Subtract \epsilon from both sides.

$$x\epsilon +cx=a-\epsilon$$

Subtract x\epsilon from both sides.

$$cx=a-\epsilon -x\epsilon$$

The equation is in standard form.

$$xc=-x\epsilon +a-\epsilon$$

Divide both sides by x.

$$\frac{xc}{x}=\frac{-x\epsilon +a-\epsilon }{x}$$

Dividing by x undoes the multiplication by x.

$$c=\frac{-x\epsilon +a-\epsilon }{x}$$

Solve for c

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

Steps for Solving Linear Equation

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

$$\epsilon +x\epsilon +cx=a$$

Subtract \epsilon from both sides.

$$x\epsilon +cx=a-\epsilon$$

Subtract x\epsilon from both sides.

$$cx=a-\epsilon -x\epsilon$$

The equation is in standard form.

$$xc=-x\epsilon +a-\epsilon$$

Divide both sides by x.

$$\frac{xc}{x}=\frac{-x\epsilon +a-\epsilon }{x}$$

Dividing by x undoes the multiplication by x.

$$c=\frac{-x\epsilon +a-\epsilon }{x}$$

Solve for a

$$a=cx+x\epsilon +\epsilon$$