Solve S=p-2r/2p+4

$$S = \frac { p - 2 r } { 2 p + 4 }$$

Solve for p

$$\left\{\begin{matrix}p=-\frac{2\left(r+2S\right)}{2S-1}\text{, }&r\neq -1\text{ and }S\neq \frac{1}{2}\\p\neq -2\text{, }&S=\frac{1}{2}\text{ and }r=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable p cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by 2\left(p+2\right).

$$S\times 2\left(p+2\right)=p-2r$$

Use the distributive property to multiply S\times 2 by p+2.

$$2Sp+2S\times 2=p-2r$$

Multiply 2 and 2 to get 4.

$$2Sp+4S=p-2r$$

Subtract p from both sides.

$$2Sp+4S-p=-2r$$

Subtract 4S from both sides.

$$2Sp-p=-2r-4S$$

Combine all terms containing p.

$$\left(2S-1\right)p=-2r-4S$$

Divide both sides by 2S-1.

$$\frac{\left(2S-1\right)p}{2S-1}=\frac{-2r-4S}{2S-1}$$

Dividing by 2S-1 undoes the multiplication by 2S-1.

$$p=\frac{-2r-4S}{2S-1}$$

Divide -2r-4S by 2S-1.

$$p=-\frac{2\left(r+2S\right)}{2S-1}$$

Variable p cannot be equal to -2.

$$p=-\frac{2\left(r+2S\right)}{2S-1}\text{, }p\neq -2$$

Solve for S

$$S=-\frac{2r-p}{2\left(p+2\right)}$$

$$p\neq -2$$