\(x^2\left(x+1\right)+2x\left(x+1\right)=0\)
\(\Leftrightarrow\left(x^2+2x\right)\left(x+1\right)=0\)
\(\Leftrightarrow x\left(x+2\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+2=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-2\\x=-1\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=0\\x=-2\\x=-1\end{matrix}\right.\)
Ta có:\(x^2\left(x+1\right)+2x\left(x+1\right)=0\)
\(\Rightarrow\left(x^2+2x\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x^2+2x=0\\x+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x\left(x+2\right)=0\\x=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\x+2=0\end{matrix}\right.\\x=-1\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\\x=-1\end{matrix}\right.\)
Vậy \(x\in\left\{0;-1;-2\right\}\)