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