CR-MO 2010 Problem 4

Find all integer solutions $(a,b)$ of the equation $(a+b+3)^2 + 2ab = 3ab(a+2)(b+2)$

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.