`x^3+x^2 +x+1=0`
`<=> x^2(x+1) + (x+1)=0`
`<=>(x+1)(x^2+1)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x^2+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0-1\\x^2=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x\notin\varnothing\end{matrix}\right.\)
\(=x^2\left(x+1\right)+\left(x+1\right)=0< =>\left(x^2+1\right)\left(x+1\right)=0< =>\left[{}\begin{matrix}x+1=0\\x^2+1=0\end{matrix}\right.< =>x=-1}\)
\(< =>x^2\left(x+1\right)+\left(x+1\right)=0< =>\left[{}\begin{matrix}x+1=0\\x^2+1=0\end{matrix}\right.< =>x=-1}\)
\(x^3+x^2+x+1=0\)
\(<=>x(x^2+x+1+1)=0\)
\(<=>x(x^2+x+2)=0\)
\(<=>[x=0<=>[x=0\)
\(<=>(x^2+x+2)=0<=>[x=-1\)
