Whoops, I didn't remember you were looking for real solutions.

I don't see why you set [latex] x^3-7x^2+14x-8=12 [/latex], since it isn't said that this polynomial is the volume. I'd suggest factorising [latex] (x^3-7x^2+14x-8) [/latex] instead, and reading off the dimensions of the box from the factorization. I think that is what is asked for.

edit: Nope that doesn't make sense either. You were of course correct.