Solve 3pq(p-q)=3p^2q-3p

$$3 p q ( p - q ) = 3 p ^ { 2 } q - 3 p$$

Solve for p (complex solution)

$$\left\{\begin{matrix}\\p=0\text{, }&\text{unconditionally}\\p\in \mathrm{C}\text{, }&q=1\text{ or }q=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3pq by p-q.

$$3qp^{2}-3pq^{2}=3p^{2}q-3p$$

Subtract 3p^{2}q from both sides.

$$3qp^{2}-3pq^{2}-3p^{2}q=-3p$$

Combine 3qp^{2} and -3p^{2}q to get 0.

$$-3pq^{2}=-3p$$

Add 3p to both sides.

$$-3pq^{2}+3p=0$$

Combine all terms containing p.

$$\left(-3q^{2}+3\right)p=0$$

The equation is in standard form.

$$\left(3-3q^{2}\right)p=0$$

Divide 0 by -3q^{2}+3.

$$p=0$$

Solve for p

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

Steps for Solving Linear Equation

Use the distributive property to multiply 3pq by p-q.

$$3qp^{2}-3pq^{2}=3p^{2}q-3p$$

Subtract 3p^{2}q from both sides.

$$3qp^{2}-3pq^{2}-3p^{2}q=-3p$$

Combine 3qp^{2} and -3p^{2}q to get 0.

$$-3pq^{2}=-3p$$

Add 3p to both sides.

$$-3pq^{2}+3p=0$$

Combine all terms containing p.

$$\left(-3q^{2}+3\right)p=0$$

The equation is in standard form.

$$\left(3-3q^{2}\right)p=0$$

Divide 0 by -3q^{2}+3.

$$p=0$$

Solve for q (complex solution)

$$\left\{\begin{matrix}\\q=1\text{; }q=-1\text{, }&\text{unconditionally}\\q\in \mathrm{C}\text{, }&p=0\end{matrix}\right.$$

Solve for q

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