The passenger section of a train has width 2x-7, length 2x+3, and height x-2, with all dimensions in metres. Solve a polynomial equation to determine the dimensions of the section of the train if the volume is 117 m^3.

I tried this and I got the expanded equation 4x^3-16x^2-5x-75. When I tried solving it, it was unfactorable, but the answer at the back has whole number answers.

Can somebody help me please?