Solve p=5t+pq

$$p = 5 t + p q$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{5t}{1-q}\text{, }&q\neq 1\\p\in \mathrm{C}\text{, }&t=0\text{ and }q=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract pq from both sides.

$$p-pq=5t$$

Combine all terms containing p.

$$\left(1-q\right)p=5t$$

Divide both sides by -q+1.

$$\frac{\left(1-q\right)p}{1-q}=\frac{5t}{1-q}$$

Dividing by -q+1 undoes the multiplication by -q+1.

$$p=\frac{5t}{1-q}$$

Solve for q (complex solution)

$$\left\{\begin{matrix}q=\frac{p-5t}{p}\text{, }&p\neq 0\\q\in \mathrm{C}\text{, }&p=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5t+pq=p$$

Subtract 5t from both sides.

$$pq=p-5t$$

Divide both sides by p.

$$\frac{pq}{p}=\frac{p-5t}{p}$$

Dividing by p undoes the multiplication by p.

$$q=\frac{p-5t}{p}$$

Solve for p

$$\left\{\begin{matrix}p=\frac{5t}{1-q}\text{, }&q\neq 1\\p\in \mathrm{R}\text{, }&t=0\text{ and }q=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract pq from both sides.

$$p-pq=5t$$

Combine all terms containing p.

$$\left(1-q\right)p=5t$$

Divide both sides by -q+1.

$$\frac{\left(1-q\right)p}{1-q}=\frac{5t}{1-q}$$

Dividing by -q+1 undoes the multiplication by -q+1.

$$p=\frac{5t}{1-q}$$

Solve for q

$$\left\{\begin{matrix}q=\frac{p-5t}{p}\text{, }&p\neq 0\\q\in \mathrm{R}\text{, }&p=0\text{ and }t=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$5t+pq=p$$

Subtract 5t from both sides.

$$pq=p-5t$$

Divide both sides by p.

$$\frac{pq}{p}=\frac{p-5t}{p}$$

Dividing by p undoes the multiplication by p.

$$q=\frac{p-5t}{p}$$