Cubic Equation, 1

Author:
Ryan Hirst
Working through the problem of solving the cubic, the question arises, suppose I remove the offset? That is, I have which is the same same as ...shifted to the right or left by some unknown number of units. Writing , the first root is 0, and the last two roots are given by the quadratic equation. If we write g(x) = f(x-t), is it possible to solve for the mystery offset t and the new mystery coefficients?