The volume of a prism is base area times height.
We need to find the factors of the expression: 6x³+38x²-28x=2x(3x²+19x-14)=2x(3x-2)(x+7).
So the dimensions could be 2x by 3x-2 by x+7.
The dimensions could also be: x by 2(3x-2) by x+7 or x by 3x-2 by 2(x+7).
For example, if x=1, the dimensions could be (2 by 1 by 8) or (1 by 1 by 16), volume is 16 cubic units.
If x=3, the dimensions could be (6 by 7 by 10), (3 by 14 by 10) or (3 by 7 by 20), volume is 420 cubic units.