Ta có: \(8-n^2-6n⋮n+6\)
\(\Leftrightarrow-\left(-8+n^2+6n\right)⋮n+6\)
\(\Leftrightarrow-\left(n^2+12n-6m+36-44\right)⋮n+6\)
\(\Leftrightarrow-\left[\left(n+6\right)^2+\left(-6n-44\right)\right]⋮n+6\)
\(\Leftrightarrow-\left(n+6\right)^2-\left(-6n-44\right)⋮n+6\)
\(\Leftrightarrow-\left(n+6\right)^2+\left(6n+44\right)⋮n+6\)
Vì \(-\left(n+6\right)^2⋮n+6\)
nên \(6n+44⋮n+6\)
\(\Leftrightarrow6n+36+8⋮n+6\)
Vì \(6n+36⋮n+6\)
nên \(8⋮n+6\)
\(\Leftrightarrow n+6\inƯ\left(8\right)\)
\(\Leftrightarrow n+6\in\left\{1;-1;2;-2;4;-4;8;-8\right\}\)
hay \(n\in\left\{-5;-7;-4;-8;-2;-10;2;-14\right\}\)(tm)
Vậy: \(n\in\left\{-5;-7;-4;-8;-2;-10;2;-14\right\}\)