Solve for h S=2Lw+2wh+5(hL)

$S = 2 L w + 2 w h + 5 (h L)$

Step 1

Rewrite the equation as $2 L w + 2 w h + 5 h L = S$ .

$2 L w + 2 w h + 5 h L = S$

Step 2

Subtract $2 L w$ from both sides of the equation.

$2 w h + 5 h L = S - 2 L w$

Step 3

Factor $h$ out of $2 w h + 5 h L$ .

Factor $h$ out of $2 w h$ .

$h (2 w) + 5 h L = S - 2 L w$

Factor $h$ out of $5 h L$ .

$h (2 w) + h (5 L) = S - 2 L w$

Factor $h$ out of $h (2 w) + h (5 L)$ .

$h (2 w + 5 L) = S - 2 L w$

Step 4

Divide each term in $h (2 w + 5 L) = S - 2 L w$ by $2 w + 5 L$ and simplify.

Divide each term in $h (2 w + 5 L) = S - 2 L w$ by $2 w + 5 L$ .

$\frac{h (2 w + 5 L)}{2 w + 5 L} = \frac{S}{2 w + 5 L} + \frac{- 2 L w}{2 w + 5 L}$

Simplify the left side.

Cancel the common factor of $2 w + 5 L$ .

Cancel the common factor.

$\frac{h (2 w + 5 L)}{2 w + 5 L} = \frac{S}{2 w + 5 L} + \frac{- 2 L w}{2 w + 5 L}$

Divide $h$ by $1$ .

$h = \frac{S}{2 w + 5 L} + \frac{- 2 L w}{2 w + 5 L}$

Simplify the right side.

Combine the numerators over the common denominator.

$h = \frac{S - 2 L w}{2 w + 5 L}$