\(4x^3-3=29\\ \Rightarrow4x^3=32\\ \Rightarrow x^3=8\\ \Rightarrow x=2\)
\(\dfrac{x+16}{9}=\dfrac{2+16}{9}=2\\\Rightarrow\dfrac{y-15}{-16}=\dfrac{z+49}{25}=2\\ \Rightarrow\left\{{}\begin{matrix}y-15=2.\left(-16\right)=-32\\z+49=2.25=50\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-17\\z=1\end{matrix}\right.\)