$a)_{}$ $2x.(x+2)-3.(x+2)=0_{}$
$⇔(2x-3)(x+2)=0_{}$
$⇔_{}$ \(\left[ \begin{array}{l}2x-3=0\\x+2=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=\frac{3}{2}\\x=-2\end{array} \right.\)
$b)_{}$ $5x^2.(x+1)-10x.(x+1)=0_{}$
$⇔(5x^2-10x)(x+1)=0_{}$
$⇔5x.(x-2)(x+1)=0_{}$
$+)5x=0_{}$ $⇔_{}$ $x=0_{}$
$⇔_{}$ \(\left[ \begin{array}{l}x-2=0\\x+1=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=2\\x=-1\end{array} \right.\)
$Vậy_{}$ $x_{1}=0;$ $x_{2}=2$ $;x_{3}=-1$
$c)_{}$ $4.(x-5)^2-(x-5)=0_{}$
$⇔(x-5).[ 4.(x-5)-1]=0_{}$
$⇔(x-5).(4x-20-1)=0_{}$
$⇔(x-5)(4x-21)_{}$
$⇔_{}$ \(\left[ \begin{array}{l}x-5=0\\4x-21=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=5\\x=\frac{21}{4}\end{array} \right.\)
$d)_{}$ $3x^2.(2x-3)-9x.(3-2x)=0_{}$
$⇔6x^3-9x^2-27x+18x^2=0_{}$
$⇔6x^3+9x^2-27x=0_{}$
$⇔3x.(2x^2+3x-9)=0_{}$
$⇔3x.(2x^2+6x-3x-9)=0_{}$
$⇔3x.[ 2x.(x+3)-3.(x+3)]=0_{}$
$⇔3x.(x+3)(2x-3)=0_{}$
$+)_{}$ $3x=0_{}$ $⇔x=0_{}$
$⇔_{}$ \(\left[ \begin{array}{l}x+3=0\\2x-3=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=-3\\x=\frac{3}{2}\end{array} \right.\)
$Vậy_{}$ $x_{1}=0;$ $x_{2}=-3;$ $x_{3}=$ $\frac{3}{2}$
$e)_{}$ $x.(x-2)-3.(2-x)=0_{}$
$⇔x.(x-2)+3.(x-2)=0_{}$
$⇔(x-2)(x+3)=0_{}$
$⇔_{}$ \(\left[ \begin{array}{l}x-2=0\\x+3=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=2\\x=-3\end{array} \right.\)
$Vậy_{}$ $x_{1}=2;$ $x_{2}=-3$
$f)_{}$ $2.(x-2)^2-x.(2-x)=0_{}$
$⇔2.(x-2)^2-x.[ -(x-2)]=0_{}$
$⇔2.(x-2)^2+x.(x-2)=0_{}$
$⇔(x-2).[ 2.(x-2)+x]=0_{}$
$⇔(x-2)(2x-4+x)=0_{}$
$⇔(x-2)(3x-4)=0_{}$
$⇔_{}$ \(\left[ \begin{array}{l}x-2=0\\3x-4=0\end{array} \right.\) $⇔_{}$ \(\left[ \begin{array}{l}x=2\\x=\frac{4}{3}\end{array} \right.\)
