\(\left(x+4\right)⋮\left(2x+1\right)\Rightarrow2\left(x+4\right)=2x+8=2x+1+7⋮\left(2x+1\right)\Leftrightarrow7⋮\left(2x+1\right)\)
\(\Leftrightarrow2x+1\inƯ\left(7\right)=\left\{-7,-1,1,7\right\}\Leftrightarrow x\in\left\{-4,-1,0,3\right\}\).
Thử lại đều thỏa mãn.