Working through the problem of solving the cubic, the question arises, [i]suppose I remove the offset?[/i] That is, I have [br][math]\;\;\; f(x) = x³+ c_2x² + c_1 x + c_0,[/math][br]which is the same same as[br][math]\;\;\; g(x) = x³+ d_2x² + d_1 x,[/math][br][br]...shifted to the right or left by some unknown number of units.[br]Writing [math]{\small g(x) = x(x² + d_2x + d_1),} [/math], the first root is 0, and the last two roots are given by the quadratic equation. [br][br]If we write g(x) = f(x-t), is it possible to solve for the mystery offset [i]t[/i] and the new mystery coefficients?