\(\frac{x}{2}=\frac{y}{5}\Leftrightarrow\frac{x}{6}=\frac{y}{15}\)
\(\frac{y}{3}=\frac{z}{2}\Leftrightarrow\frac{y}{15}=\frac{z}{10}\)
\(\Leftrightarrow\frac{x}{6}=\frac{y}{15}=\frac{z}{10}=\frac{x+y+z}{6+15+10}=\frac{-62}{31}=-2\)
\(\Rightarrow x=\left(-2\right).6=-12\)
\(y=\left(-2\right).15=-30\)
\(z=\left(-2\right).10=-20\)