Is there any transformation for the polynomial $x^4+ax^3+bx+1$ to either one of these forms $x^4+cx+d$ or $x^4+cx^3+d$ ? (like brioschi quintic form)

Question

I would like to transform the degree 4 polynomial to the degree 4 polynomial with specific powers of x removed. something like depressed cubic form or Brioschi quintic. Do we have any special transformation for quartic polynomials?