If there exist integer solution they must be factors of 24. Determine all factors of

24 : ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24

Check if one of these 16 fctors is a solution of the equation. I've found x = 2.

Use synthetic division to cancel out the factor (x - 2). I've got:

Solve the quadratic

for x to get the last 2 solutions of the equation