Finding dimensions of a rectangular box to optimize volume

A rectangular box (base is not square) with an open top must have a length of 3ft, and a surface area of $16f{t}^{2}$. Compute the dimensions of the box that will maximize its volume.

I am going wrong somewhere but I can't see where. I have set $2(3h+3w+hw)=16$ and my optimization equation is $v=hwl$. I set $w=\frac{8-3h}{3+h}$ and plug into the optimization equation. Calculating v' gives me $\frac{9{h}^{2}-84h+72}{{(3+h)}^{2}}$,but setting that equal to zero does not give me the answer. I need for h, which is 1.

A rectangular box (base is not square) with an open top must have a length of 3ft, and a surface area of $16f{t}^{2}$. Compute the dimensions of the box that will maximize its volume.

I am going wrong somewhere but I can't see where. I have set $2(3h+3w+hw)=16$ and my optimization equation is $v=hwl$. I set $w=\frac{8-3h}{3+h}$ and plug into the optimization equation. Calculating v' gives me $\frac{9{h}^{2}-84h+72}{{(3+h)}^{2}}$,but setting that equal to zero does not give me the answer. I need for h, which is 1.