UA-UMO 1997 Problem 114

The equation $ax^3+bx^2+cx+d=0$ has three distinct solutions. How many distinct solutions does the following equation have:

$4(ax^3+bx^2+cx+d)(3ax+b)=(3ax^2+2bx+c)^2?$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.