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