Revisiting the general cubic: a simplification of Cardano's solution

Given a polynomial equation x(3) + ax(2) + bx + c = 0 of degree 3 with real coefficients, we may translate the variable by replacing x with x - to make the quadratic term vanish. We then obtain a simpler equation x(3) + px + q = 0 where Therefore, in order to solve a polynomial equation of degree 3, it is sufficient to solve equations of the form x(3) + px + q = 0.