Ta có: 4n+7= 2.( 2n+1)+5
Do đó: 4n+7 chia hết cho 2n+1 <=> 5 chia hết cho 2n+1 <=> 2n+1 thuộc Ư(5) thuộc +_1;+_5
Do đó: 2n+1=1 => 2n= 0 => n= 0
2n+1=-1 => 2n= 2 => n= -1
2n+1=5 => 2n= 4 => n= 2
2n+1=-5 => 2n= -6 => n= -3
Vậy n thuộc 0;-1;2;-3
Giải xong rồi hihi 
\(4n+7⋮2n+1\)
\(\Rightarrow4n+7-\left[2\left(2n+1\right)\right]⋮2n+1\)
\(\Rightarrow4n+7-\left(4n+2\right)⋮2n+1\)
\(\Rightarrow4n+7-4n-2⋮2n+1\)
\(\Rightarrow5⋮2n+1\)
\(\Rightarrow2n+1\inƯ\left(5\right)=\left\{1;5\right\}\)
\(\Rightarrow2n\in\left\{0;4\right\}\)
\(\Rightarrow n\in\left\{0;2\right\}\)
Vậy \(n\in\left\{0;2\right\}\)
