\(x^3-7x+6=0\)
\(\Leftrightarrow x^2\left(x+3\right)-3x\left(x+3\right)+2\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+2\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left[x\left(x-2\right)-1\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-2\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2\\x=1\end{matrix}\right.\)
<=>\(\left(x+3\right)\left(x-2\right)\left(x-1\right)=0\)
<=>\(\left[{}\begin{matrix}x+3=0\\x-2=0\\x-1=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=-3\\x=2\\x=1\end{matrix}\right.\)
\(x^3-7x\cdot+6=0\\ \Leftrightarrow x^3-x^2+x^2-x-6x+6=0\\ \Leftrightarrow\left(x-1\right)\left(x^2+x-6\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+3\right)=0\\ \Leftrightarrow\left\{{}\begin{matrix}x=1\\x=2\\x=-3\end{matrix}\right.\)
\(x^3-7x+6=0\)
\(=x^3-x-6x+6=0\)
\(=x\left(x^2-1\right)-6\left(x-1\right)=0\)
\(=x\left(x-1\right)\left(x-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left[x\left(x+1\right)-6\right]=0\)
\(\Rightarrow\left\{{}\begin{matrix}x-1=0\\x\left(x+1\right)-6=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\2\end{matrix}\right.\)
\(x^3-7x+6=0\)
\(\Leftrightarrow x^3-x-6x+6=0\)
\(\Leftrightarrow x\left(x^2-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)\left(x-1\right)-6\left(x-1\right)=0\)
\(\Leftrightarrow\left[x\left(x+1\right)-6\right]\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2+x-6\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(x^2+3x-2x-6\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[x\left(x+3\right)-2\left(x+3\right)\right]\left(x-1\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-2\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x-2=0\\x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2\\x=1\end{matrix}\right.\)