\(\left(3n+7\right)⋮\left(2n-5\right)\Rightarrow\left(6n+14\right)⋮\left(2n-5\right)\)
\(\Rightarrow3\left(2n-5\right)+29⋮\left(2n-5\right)\)
\(\Rightarrow\left(2n-5\right)\inƯ\left(29\right)=\left\{-29;-1;1;29\right\}\)
\(\Rightarrow n\in\left\{-12;2;3;17\right\}\)