Solve x^2-x=mx-r

$$x ^ { 2 } - x = m x - r$$

Solve for m

$$\left\{\begin{matrix}m=x+\frac{r}{x}-1\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&r=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$mx-r=x^{2}-x$$

Add r to both sides.

$$mx=x^{2}-x+r$$

The equation is in standard form.

$$xm=x^{2}-x+r$$

Divide both sides by x.

$$\frac{xm}{x}=\frac{x^{2}-x+r}{x}$$

Dividing by x undoes the multiplication by x.

$$m=\frac{x^{2}-x+r}{x}$$

Divide x^{2}-x+r by x.

$$m=x+\frac{r}{x}-1$$

Solve for r

$$r=x\left(1+m-x\right)$$

Steps for Solving Linear Equation

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

$$mx-r=x^{2}-x$$

Subtract mx from both sides.

$$-r=x^{2}-x-mx$$

The equation is in standard form.

$$-r=x^{2}-mx-x$$

Divide both sides by -1.

$$\frac{-r}{-1}=\frac{x\left(x-m-1\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$r=\frac{x\left(x-m-1\right)}{-1}$$

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

$$r=x+mx-x^{2}$$