Solve for h s=4Lw+4wh+5(hL)

$s = 4 L w + 4 w h + 5 (h L)$

Step 1

Rewrite the equation as $4 L w + 4 w h + 5 h L = s$ .

$4 L w + 4 w h + 5 h L = s$

Step 2

Subtract $4 L w$ from both sides of the equation.

$4 w h + 5 h L = s - 4 L w$

Step 3

Factor $h$ out of $4 w h + 5 h L$ .

Factor $h$ out of $4 w h$ .

$h (4 w) + 5 h L = s - 4 L w$

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

$h (4 w) + h (5 L) = s - 4 L w$

Factor $h$ out of $h (4 w) + h (5 L)$ .

$h (4 w + 5 L) = s - 4 L w$

Step 4

Divide each term in $h (4 w + 5 L) = s - 4 L w$ by $4 w + 5 L$ and simplify.

Divide each term in $h (4 w + 5 L) = s - 4 L w$ by $4 w + 5 L$ .

$\frac{h (4 w + 5 L)}{4 w + 5 L} = \frac{s}{4 w + 5 L} + \frac{- 4 L w}{4 w + 5 L}$

Simplify the left side.

Cancel the common factor of $4 w + 5 L$ .

Cancel the common factor.

$\frac{h (4 w + 5 L)}{4 w + 5 L} = \frac{s}{4 w + 5 L} + \frac{- 4 L w}{4 w + 5 L}$

Divide $h$ by $1$ .

$h = \frac{s}{4 w + 5 L} + \frac{- 4 L w}{4 w + 5 L}$

Simplify the right side.

Combine the numerators over the common denominator.

$h = \frac{s - 4 L w}{4 w + 5 L}$