Solve for L S=2HW+2HL+2WL

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

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

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

Subtract $2 H W$ from both sides of the equation.

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

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

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

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

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

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $H + W$ .

Cancel the common factor.

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

Divide $L$ by $1$ .

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

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 H W$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

To write $- \frac{H W}{H + W}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $2 (H + W)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{H W}{H + W}$ by $\frac{2}{2}$ .

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

Reorder the factors of $(H + W) \cdot 2$ .

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

Combine the numerators over the common denominator.

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

Multiply $2$ by $- 1$ .

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

Solve for L S=2HW+2HL+2WL

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