Evaluate Using the Given Value S=4LW+4wh+3(hL) ; for h

$S = 4 L W + 4 w h + 3 (h L)$ ; for $h$

Rewrite the equation as $4 L W + 4 w h + 3 h L = S$ .

$4 L W + 4 w h + 3 h L = S$

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

$4 w h + 3 h L = S - 4 L W$

Factor $h$ out of $4 w h + 3 h L$ .

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

$h (4 w) + 3 h L = S - 4 L W$

Factor $h$ out of $3 h L$ .

$h (4 w) + h (3 L) = S - 4 L W$

Factor $h$ out of $h (4 w) + h (3 L)$ .

$h (4 w + 3 L) = S - 4 L W$

Divide each term in $h (4 w + 3 L) = S - 4 L W$ by $4 w + 3 L$ and simplify.

Divide each term in $h (4 w + 3 L) = S - 4 L W$ by $4 w + 3 L$ .

$\frac{h (4 w + 3 L)}{4 w + 3 L} = \frac{S}{4 w + 3 L} + \frac{- 4 L W}{4 w + 3 L}$

Simplify the left side.

Cancel the common factor of $4 w + 3 L$ .

Cancel the common factor.

$\frac{h (4 w + 3 L)}{4 w + 3 L} = \frac{S}{4 w + 3 L} + \frac{- 4 L W}{4 w + 3 L}$

Divide $h$ by $1$ .

$h = \frac{S}{4 w + 3 L} + \frac{- 4 L W}{4 w + 3 L}$

Simplify the right side.

Combine the numerators over the common denominator.

$h = \frac{S - 4 L W}{4 w + 3 L}$