a: \(x^2\left(x+1\right)-x-1=0\)
=>\(x^2\left(x+1\right)-\left(x+1\right)=0\)
=>\(\left(x+1\right)\left(x^2-1\right)=0\)
=>\(\left(x+1\right)^2\cdot\left(x-1\right)=0\)
=>\(\left[{}\begin{matrix}\left(x+1\right)^2=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x+1=0\\x-1=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-1\\x=1\end{matrix}\right.\)
b: \(x^2-x=-3x^2+3x\)
=>\(x^2-x+3x^2-3x=0\)
=>\(4x^2-4x=0\)
=>\(x^2-x=0\)
=>x(x-1)=0
=>\(\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
c: \(2x^2\left(x-1\right)-x=-x^2\)
=>\(2x^2\left(x-1\right)+x^2-x=0\)
=>\(2x^2\left(x-1\right)+x\left(x-1\right)=0\)
=>\(\left(x-1\right)\left(2x^2+x\right)=0\)
=>\(x\cdot\left(x-1\right)\left(2x+1\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x-1=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-\dfrac{1}{2}\end{matrix}\right.\)
d: \(\left(x-2\right)\cdot\left(x^2+4\right)=5\left(x^2-2x\right)\)
=>\(\left(x-2\right)\left(x^2+4\right)=5x\left(x-2\right)\)
=>\(\left(x-2\right)\cdot\left(x^2-5x+4\right)=0\)
=>\(\left(x-2\right)\left(x-1\right)\left(x-4\right)=0\)
=>\(\left[{}\begin{matrix}x-2=0\\x-1=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=1\\x=4\end{matrix}\right.\)
