Solve for L S=2LW+2LH

$S = 2 L W + 2 L H$

Rewrite the equation as $2 L W + 2 L H = S$ .

$2 L W + 2 L H = S$

Factor $2 L$ out of $2 L W + 2 L H$ .

Factor $2 L$ out of $2 L W$ .

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

Factor $2 L$ out of $2 L H$ .

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

Factor $2 L$ out of $2 L (W) + 2 L (H)$ .

$2 L (W + H) = S$

Divide each term in $2 L (W + H) = S$ by $2 (W + H)$ and simplify.

Divide each term in $2 L (W + H) = S$ by $2 (W + H)$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $W + H$ .

Cancel the common factor.

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

Divide $L$ by $1$ .

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