Question 946856
Just to begin,

w, the width
L, the length
L=w+15
h, the side length of the squares cut out
h=3
v, the volume of the box when the flaps folded
v=648
The only true unknown here is the width, w.


The bottom area will be  {{{(w-2h)(L-2h)=wL-2Lh-2wh+4h^2}}};
The volume will be {{{(wL-2Lh-2wh+4h^2)*h=v}}};
Substitute for L, and simplify.  This should be a quadratic equation in the symbolic form with w being the only unknown variable.  


You would solve the resulting quadratic equation in w, and plugin the known values any time you are ready.