Solve p=4ps+4q-6

$$p = 4 p s + 4 q - 6$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{2\left(3-2q\right)}{1-4s}\text{, }&s\neq \frac{1}{4}\\p\in \mathrm{C}\text{, }&q=\frac{3}{2}\text{ and }s=\frac{1}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4ps from both sides.

$$p-4ps=4q-6$$

Combine all terms containing p.

$$\left(1-4s\right)p=4q-6$$

Divide both sides by -4s+1.

$$\frac{\left(1-4s\right)p}{1-4s}=\frac{4q-6}{1-4s}$$

Dividing by -4s+1 undoes the multiplication by -4s+1.

$$p=\frac{4q-6}{1-4s}$$

Divide 4q-6 by -4s+1.

$$p=\frac{2\left(2q-3\right)}{1-4s}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{2\left(3-2q\right)}{1-4s}\text{, }&s\neq \frac{1}{4}\\p\in \mathrm{R}\text{, }&q=\frac{3}{2}\text{ and }s=\frac{1}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 4ps from both sides.

$$p-4ps=4q-6$$

Combine all terms containing p.

$$\left(1-4s\right)p=4q-6$$

Divide both sides by -4s+1.

$$\frac{\left(1-4s\right)p}{1-4s}=\frac{4q-6}{1-4s}$$

Dividing by -4s+1 undoes the multiplication by -4s+1.

$$p=\frac{4q-6}{1-4s}$$

Divide 4q-6 by -4s+1.

$$p=\frac{2\left(2q-3\right)}{1-4s}$$

Solve for q

$$q=\frac{6+p-4ps}{4}$$

Steps for Solving Linear Equation

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

$$4ps+4q-6=p$$

Subtract 4ps from both sides.

$$4q-6=p-4ps$$

Add 6 to both sides.

$$4q=p-4ps+6$$

The equation is in standard form.

$$4q=6+p-4ps$$

Divide both sides by 4.

$$\frac{4q}{4}=\frac{6+p-4ps}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$q=\frac{6+p-4ps}{4}$$

Divide p-4ps+6 by 4.

$$q=-ps+\frac{p}{4}+\frac{3}{2}$$