Solve +4(p+q)x+p+b=0

$$+ 4 ( p + q ) x + p + b = 0$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=-\frac{4qx+b}{4x+1}\text{, }&x\neq -\frac{1}{4}\\p\in \mathrm{C}\text{, }&q=b\text{ and }x=-\frac{1}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by p+q.

$$\left(4p+4q\right)x+p+b=0$$

Use the distributive property to multiply 4p+4q by x.

$$4px+4qx+p+b=0$$

Subtract 4qx from both sides. Anything subtracted from zero gives its negation.

$$4px+p+b=-4qx$$

Subtract b from both sides.

$$4px+p=-4qx-b$$

Combine all terms containing p.

$$\left(4x+1\right)p=-4qx-b$$

Divide both sides by 4x+1.

$$\frac{\left(4x+1\right)p}{4x+1}=\frac{-4qx-b}{4x+1}$$

Dividing by 4x+1 undoes the multiplication by 4x+1.

$$p=\frac{-4qx-b}{4x+1}$$

Divide -4qx-b by 4x+1.

$$p=-\frac{4qx+b}{4x+1}$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{4qx+b}{4x+1}\text{, }&x\neq -\frac{1}{4}\\p\in \mathrm{R}\text{, }&q=b\text{ and }x=-\frac{1}{4}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by p+q.

$$\left(4p+4q\right)x+p+b=0$$

Use the distributive property to multiply 4p+4q by x.

$$4px+4qx+p+b=0$$

Subtract 4qx from both sides. Anything subtracted from zero gives its negation.

$$4px+p+b=-4qx$$

Subtract b from both sides.

$$4px+p=-4qx-b$$

Combine all terms containing p.

$$\left(4x+1\right)p=-4qx-b$$

Divide both sides by 4x+1.

$$\frac{\left(4x+1\right)p}{4x+1}=\frac{-4qx-b}{4x+1}$$

Dividing by 4x+1 undoes the multiplication by 4x+1.

$$p=\frac{-4qx-b}{4x+1}$$

Divide -4qx-b by 4x+1.

$$p=-\frac{4qx+b}{4x+1}$$

Solve for b

$$b=-\left(4x\left(p+q\right)+p\right)$$