Solve Ax=xf-x

$$A x = x f - x$$

Solve for A (complex solution)

$$\left\{\begin{matrix}\\A=f-1\text{, }&\text{unconditionally}\\A\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xA=fx-x$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{x\left(f-1\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{x\left(f-1\right)}{x}$$

Divide x\left(-1+f\right) by x.

$$A=f-1$$

Solve for f (complex solution)

$$\left\{\begin{matrix}\\f=A+1\text{, }&\text{unconditionally}\\f\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xf-x=Ax$$

Add x to both sides.

$$xf=Ax+x$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{Ax+x}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{Ax+x}{x}$$

Divide xA+x by x.

$$f=A+1$$

Solve for A

$$\left\{\begin{matrix}\\A=f-1\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xA=fx-x$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{x\left(f-1\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{x\left(f-1\right)}{x}$$

Divide x\left(-1+f\right) by x.

$$A=f-1$$

Solve for f

$$\left\{\begin{matrix}\\f=A+1\text{, }&\text{unconditionally}\\f\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$xf-x=Ax$$

Add x to both sides.

$$xf=Ax+x$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{Ax+x}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{Ax+x}{x}$$

Divide xA+x by x.

$$f=A+1$$