`a, x(x - 1) - 2(1 - x) = 0`
`⇔ x(x - 1) + 2(x - 1) = 0`
`⇔ (x + 2)(x - 1) = 0`
`⇔` \(\left[ \begin{array}{l}x+2=0\\x-1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=-2\\x=1\end{array} \right.\)
`b, 2x(x-2)-(2-x)^2=0`
`⇔ 2x(x-2)-(x-2)^2=0`
`⇔ (x-2)(2x-x+2)=0`
`⇔ (x-2)(x+2)=0`
`⇔` \(\left[ \begin{array}{l}x-2=0\\x+2=0\end{array} \right.\) `⇔`\(\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.\)
`c,(x-3)^3+3-x=0`
`⇔ (x-3)^3-(x-3)=0`
`⇔ (x-3)[(x-3)^2-1]=0`
`⇔ (x-3)(x-3-1)(x-3+1)=0`
`⇔ (x-3)(x-4)(x-2)=0`
`⇔` \(\left[ \begin{array}{2}x-3=0\\x-4=0\\x-2=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{2}x=3\\x=4\\x=2\end{array} \right.\)
`d, 5x(x-2)-(2-x)=0`
`⇔ 5x(x-2) + (x-2)=0`
`⇔ (5x + 1)(x-2)=0`
`⇔` \(\left[ \begin{array}{l}5x+1=0\\x-2=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{-1}{5}\\x=2\end{array} \right.\)
`e, 5x(x-2000)-x+2000=0`
`⇔5x(x-2000)-(x-2000)=0`
`⇔(5x-1)(x-2000)=0`
`⇔` \(\left[ \begin{array}{l}5x-1=0\\x-2000=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=\dfrac{1}{5}\\x=2000\end{array} \right.\)
`g, x^2 -4x=0`
`⇔x(x-4)=0`
`⇔` \(\left[ \begin{array}{l}x=0\\x-4=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=0\\x=4\end{array} \right.\)
`h, (1-x)^2 -1+x=0`
`⇔(1-x)^2 - (1-x)=0`
`⇔(1-x)(1-x-1)=0`
`⇔-x(1-x)=0`
`⇔` \(\left[ \begin{array}{l}-x=0\\1-x=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\)
`k, x + 6x^2 = 0`
`⇔ x(1 + 6x)=0`
`⇔` \(\left[ \begin{array}{l}x=0\\1+6x=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=0\\x=\dfrac{1}{6}\end{array} \right.\)
`m, (x+1)=(x+1)^2`
`⇔(x+1)-(x+1)^2=0`
`⇔(x+1)(1-x-1)=0`
`⇔-x(x+1)=0`
`⇔` \(\left[ \begin{array}{l}-x=0\\x+1=0\end{array} \right.\) `⇔` \(\left[ \begin{array}{l}x=0\\x=-1\end{array} \right.\)
