\[\begin{align} a\left(y-\frac{b}{3a}\right)^3 +b \left(y-\frac{b}{3a}\right)^2 + c\left(y-\frac{b}{3a}\right) + d &=0\\ ay^3-by^2+\frac{b^2}{3a}y-\frac{b^3}{27a^2}+by^2-\frac{2b^2}{3a}y+\frac{b^3}{9a^2}+cy-\frac{bc}{3a} + d &= 0\\ ay^3+\left( c-\frac{b^2}{3a} \right) y + \left( d + \frac{2b^3}{27a^2}-\frac{bc}{3a} \right) &= 0. \end{align}\]