Solve pv-v=0

$$p v - v = 0$$

Solve for p

$$\left\{\begin{matrix}\\p=1\text{, }&\text{unconditionally}\\p\in \mathrm{R}\text{, }&v=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add v to both sides. Anything plus zero gives itself.

$$pv=v$$

The equation is in standard form.

$$vp=v$$

Divide both sides by v.

$$\frac{vp}{v}=\frac{v}{v}$$

Dividing by v undoes the multiplication by v.

$$p=\frac{v}{v}$$

Divide v by v.

$$p=1$$

Solve for v

$$\left\{\begin{matrix}\\v=0\text{, }&\text{unconditionally}\\v\in \mathrm{R}\text{, }&p=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Combine all terms containing v.

$$\left(p-1\right)v=0$$

Divide 0 by p-1.

$$v=0$$