Solve c-dx=ex+f

$$c - d x = e x + f$$

Solve for d (complex solution)

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

Steps for Solving Linear Equation

Subtract c from both sides.

$$-dx=ex+f-c$$

The equation is in standard form.

$$\left(-x\right)d=ex+f-c$$

Divide both sides by -x.

$$\frac{\left(-x\right)d}{-x}=\frac{ex+f-c}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$d=\frac{ex+f-c}{-x}$$

Divide ex-c+f by -x.

$$d=-\frac{ex+f-c}{x}$$

Solve for d

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

Steps for Solving Linear Equation

Subtract c from both sides.

$$-dx=ex+f-c$$

The equation is in standard form.

$$\left(-x\right)d=ex+f-c$$

Divide both sides by -x.

$$\frac{\left(-x\right)d}{-x}=\frac{ex+f-c}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$d=\frac{ex+f-c}{-x}$$

Divide ex+f-c by -x.

$$d=-\frac{ex+f-c}{x}$$

Solve for c

$$c=dx+ex+f$$

Solution Steps

Add dx to both sides.

$$c=ex+f+dx$$