\(\dfrac{6x}{2x-1}\in Z\Rightarrow\dfrac{6x-3+3}{2x-1}\in Z\Rightarrow\dfrac{3\left(2x-1\right)+3}{2x-1}\in Z\)
\(\Rightarrow3+\dfrac{3}{2x-1}\in Z\)
\(\Rightarrow\dfrac{3}{2x-1}\in Z\)
\(\Rightarrow2x-1=Ư\left(3\right)=\left\{-3;-1;1;3\right\}\)
\(\Rightarrow x=\left\{-1;0;1;2\right\}\)