`1)`
`2x^2-3x=0`
`<=>x.(2x-3)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\2x-3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\2x=3\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=\dfrac{3}{2}\end{array} \right.\)
Vậy `S={0;3/2}`
`2)`
`x^2-9=0`
`<=>(x-3).(x+3)=0`
`<=>`\(\left[ \begin{array}{l}x-3=0\\x+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-3\end{array} \right.\)
Vậy `S={-3;3}`
`3)`
`4x^3-9x=0`
`<=>x.(4x^2-9)=0`
`<=>x.[(2x)^2-3^2]=0`
`<=>x.(2x-3).(2x+3)=0`
`<=>`\(\left[ \begin{array}{l}x=0\\2x-3=0\\2x+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\2x=3\\2x=-3\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=\dfrac{3}{2}\\x=-\dfrac{3}{2}\end{array} \right.\)
Vậy `S={0;-3/2;3/2}`
`4)`
`(x-2)^2-9=0`
`<=>(x-2)^2-3^2=0`
`<=>(x-2-3).(x-2+3)=0`
`<=>(x-5).(x+1)=0`
`<=>`\(\left[ \begin{array}{l}x-5=0\\x+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=5\\x=-1\end{array} \right.\)
Vậy `S={-1;5}`
`5)`
`(2x-5)^2-9=0`
`<=>(2x-5)^2-3^2=0`
`<=>(2x-5-3).(2x-5+3)=0`
`<=>(2x-8).(2x-2)=0`
`<=>`\(\left[ \begin{array}{l}2x-8=0\\2x-2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}2x=8\\2x=2\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=4\\x=1\end{array} \right.\)
Vậy `S={1;4}`
`6)`
`(3x+2)^2-4=0`
`<=>(3x+2)^2-2^2=0`
`<=>(3x+2-2).(3x+2+2)=0`
`<=>3x.(3x+4)=0`
`<=>`\(\left[ \begin{array}{l}3x=0\\3x+4=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\3x=-4\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=0\\x=-\dfrac{4}{3}\end{array} \right.\)
Vậy `S={-4/3;0}`
`7)`
`(2x-1)^2-16=9`
`<=>(2x-1)^2-16-9=0`
`<=>(2x-1)^2-25=0`
`<=>(2x-1-5).(2x-1+5)=0`
`<=>(2x-6).(2x+4)=0`
`<=>`\(\left[ \begin{array}{l}2x-6=0\\2x+4=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}2x=6\\2x=-4\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-2\end{array} \right.\)
Vậy `S={-2;3}`
`8)`
`(2x-3)^2+9=25`
`<=>(2x-3)^2+9-25=0`
`<=>(2x-3)^2-16=0`
`<=>(2x-3-4).(2x-3+4)=0`
`<=>(2x-7).(2x+1)=0`
`<=>`\(\left[ \begin{array}{l}2x-7=0\\2x+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}2x=7\\2x=-1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{7}{2}\\x=-\dfrac{1}{2}\end{array} \right.\)
Vậy `S={-1/2;7/2}`
`9)`
`(3x-2)^2-9=16`
`<=>(3x-2)^2-9-16=0`
`<=>(3x-2)^2-25=0`
`<=>(3x-2-5).(3x-2+5)=0`
`<=>(3x-7).(3x+3)=0`
`<=>`\(\left[ \begin{array}{l}3x-7=0\\3x+3=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}3x=7\\3x=-3\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{7}{3}\\x=-1\end{array} \right.\)
Vậy `S={-1;7/3}`
`10)`
`(2x-5)^2=9x^2`
`<=>(2x-5)^2-9x^2=0`
`<=>(2x-5)^2-(3x)^2=0`
`<=>(2x-5-3x).(2x-5+3x)=0`
`<=>(-x-5).(5x-5)=0`
`<=>`\(\left[ \begin{array}{l}-x-5=0\\5x-5=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-5\\5x=5\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-5\\x=1\end{array} \right.\)
Vậy `S={-5;1}`
`11)`
`4(3x+1)^2+16=25`
`<=>[2.(3x+1)]^2+16-25=0`
`<=>(6x+2)^2-9=0`
`<=>(6x+2-3).(6x+2+3)=0`
`<=>(6x-1).(6x+5)=0`
`<=>`\(\left[ \begin{array}{l}6x-1=0\\6x+5=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}6x=1\\6x=-5\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\dfrac{1}{6}\\x=-\dfrac{5}{6}\end{array} \right.\)
Vậy `S={1/6;-5/6}`
`12)`
`x(x-3)-2(3-x)=0`
`<=>x(x-3)+2(x-3)=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 `S={-2;3}`
`13)`
`(x-3).(2x+1)-2(2x+1)=0`
`<=>(x-3-2).(2x+1)=0`
`<=>(x-5).(2x+1)=0`
`<=>`\(\left[ \begin{array}{l}x-5=0\\2x+1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=5\\2x=-1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=5\\x=-\dfrac{1}{2}\end{array} \right.\)
Vậy `S={-1/2;5}`
