\(\dfrac{1}{3}x+\dfrac{2}{5}\left(x-1\right)=0\)
\(\Leftrightarrow\dfrac{1}{3}x+\dfrac{2}{5}x-\dfrac{2}{5}=0\)
\(\Rightarrow\dfrac{11}{15}x-\dfrac{2}{5}=0\)
\(\Rightarrow\dfrac{11}{15}x=\dfrac{-2}{5}\)
\(\Rightarrow x=\dfrac{-2}{5}.\dfrac{15}{11}\)
\(\Rightarrow x=\dfrac{-6}{11}\)