Ta có: $\left \{ {{–3n+2⋮2n+1} \atop {2n+1⋮2n+1}} \right.$⇒$\left \{ {{2.(–3n+2)⋮2n+1} \atop {-3.(2n+1)⋮2n+1}} \right.$⇒$\left \{ {{-6n+4⋮2n+1} \atop {-6n-3⋮2n+1}} \right.$
⇒(-6n+4)-(-6n-3) ⋮ 2n+1
⇒7 ⋮ 2n+1
⇒2n+1 ∈Ư(7)={±1;±7}
Với 2n+1=-1⇒n=-1
Với 2n+1=1⇒n=0
Với 2n+1=-7⇒n=-4
Với 2n+1=7⇒n=3
Vậy n ∈{-1;0;-4;3}.