Illustrate that cubic factor can be written in given form

Question

The polynomial (z) is described by (z) = z⁵ - 6z⁴ + 15z³ - 34z² + 36z - 48. Illustrate that equation (z) = 0 has roots of form z = lambda i, where lambda is real, and therefore factorize (z). Illustrate further that cubic factor of (z) can be written in form (z + a) 3 + b, where a and b are real, and therefore solve equation (z) = 0 completely.