Giải thích các bước giải:
1. 2(x+1)+x+1=0⇔2x+2+x+1=0⇔3x+3=0⇔x=-1
2.x(x-1)+x-1=0⇔(x-1)(x+1)=0⇔\(\left[ \begin{array}{l}x-1=0\\x+1=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=1\\x=-1\end{array} \right.\)
3. 2x(x-2)+2x-4=0⇔2x(x-2)+2(x-2)=0⇔(x-2)(2x+2)=0⇔\(\left[ \begin{array}{l}x-2=0\\2x+2=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=2\\x=-1\end{array} \right.\)
4. 3(x-1)-x-1=0⇔3x-3-x-1=0⇔2x=4⇔x=2
5.3x(2x-1)-2x+1=0⇔3x(2x-1)-(2x-1)=0⇔(2x-1)(3x-1)=0⇔\(\left[ \begin{array}{l}3x-1=0\\2x-1=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=1/3\\x=1/2\end{array} \right.\)
6. x-3+3x(x-3)=0⇔(x-3)(1+3x)=0⇔\(\left[ \begin{array}{l}x-3=0\\3x+1=0\end{array} \right.\) ⇔\(\left[ \begin{array}{l}x=3\\x=-1/3\end{array} \right.\)