Question

S=2(lw+lh+wh) solve for w

Answer 1

we have

$s=2(lw+lh+wh)$

Solve for w means that clear variable w

$s=2(lw+lh+wh)\\s=2lw+2lh+2wh$

Group terms that contain the variable w, and move the other terms to the opposite side of the equation

$(s-2lh)=(2lw+2wh)$

Factor the variable w

$(s-2lh)=w(2l+2h)$

Divide both sides by $(2l+2h)$

$(s-2lh)/(2l+2h)=w(2l+2h)/(2l+2h)$

$w=(s-2lh)/(2l+2h)$

therefore

the answer is

$w=(s-2lh)/(2l+2h)$

Answer 2

$S=2(lw+lh+wh)\\ S=2lw+2lh+2wh\\ S=w(2l+2h)+2lh\\ w(2l+2h)=S-2lh\\ w=\frac{S-2lh}{2l+2h}$