Solve S=2LH+2LW

$$S = 2 L H + 2 L W$$

Solve for H

$$\left\{\begin{matrix}H=-W+\frac{S}{2L}\text{, }&L\neq 0\\H\in \mathrm{R}\text{, }&S=0\text{ and }L=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2LH+2LW=S$$

Subtract 2LW from both sides.

$$2LH=S-2LW$$

Divide both sides by 2L.

$$\frac{2LH}{2L}=\frac{S-2LW}{2L}$$

Dividing by 2L undoes the multiplication by 2L.

$$H=\frac{S-2LW}{2L}$$

Divide -2LW+S by 2L.

$$H=-W+\frac{S}{2L}$$

Solve for L

$$\left\{\begin{matrix}L=\frac{S}{2\left(H+W\right)}\text{, }&H\neq -W\\L\in \mathrm{R}\text{, }&S=0\text{ and }H=-W\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2LH+2LW=S$$

Combine all terms containing L.

$$\left(2H+2W\right)L=S$$

Divide both sides by 2H+2W.

$$\frac{\left(2H+2W\right)L}{2H+2W}=\frac{S}{2H+2W}$$

Dividing by 2H+2W undoes the multiplication by 2H+2W.

$$L=\frac{S}{2H+2W}$$

Divide S by 2H+2W.

$$L=\frac{S}{2\left(H+W\right)}$$