Solve p=4(3p(p+q))

$$p = 4 ( 3 p ( p + q ) )$$

Solve for q

$$\left\{\begin{matrix}\\q=\frac{1}{12}-p\text{, }&\text{unconditionally}\\q\in \mathrm{R}\text{, }&p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply 4 and 3 to get 12.

$$p=12p\left(p+q\right)$$

Use the distributive property to multiply 12p by p+q.

$$p=12p^{2}+12pq$$

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

$$12p^{2}+12pq=p$$

Subtract 12p^{2} from both sides.

$$12pq=p-12p^{2}$$

Divide both sides by 12p.

$$\frac{12pq}{12p}=\frac{p\left(1-12p\right)}{12p}$$

Dividing by 12p undoes the multiplication by 12p.

$$q=\frac{p\left(1-12p\right)}{12p}$$

Divide p\left(1-12p\right) by 12p.

$$q=\frac{1}{12}-p$$

Solve for p

$$p=\frac{1}{12}-q$$

$$p=0$$