Đáp án+Giải thích các bước giải:

 Bài `4:`

`a)(x-2).(3x+5)=(2x-4).(x+1)`

`(x-2).(3x+5)=2.(x-2).(x+1)`

`(x-2).(3x+5)-(x-2).(2x+2)=0`

`(x-2).(3x+5-2x-2)=0`

`(x-2).(x+3)=0`

`x-2=0` hoặc `x+3=0`

`x=2` hoặc `x=-3`

Vậy `S={2;-3}`

`b)(2x+5).(x-4)=(x-5).(4-x)`

`(2x+5).(x-4)=-(x-5).(x-4)`

`(2x+5).(x-4)+(x-5).(x-4)=0`

`(x-4).(2x+5+x-5)=0`

`3x.(x-4)=0`

`3x=0` hoặc `x-4=0`

`x=0` hoặc `x=4`

Vậy `S={0;4}`

`c)9x^{2}-1=(3x+1).(2x-3)`

`(3x)^{2}-1^{2}=(3x+1).(2x-3)`

`(3x-1).(3x+1)-(3x+1).(2x-3)=0`

`(3x+1).(3x-1-2x+3)=0`

`(3x+1).(x+2)=0`

`3x+1=0` hoặc `x+2=0`

`x=-1/3` hoặc `x=-2`

Vậy `S={-1/3;-2}`

`d)2.(9x^{2}+6x+1)=(3x+1).(x-2)`

`2.[(3x)^{2}+2.3x.1+1^{2}]-(3x+1).(x-2)=0`

`2.(3x+1)^{2}-(3x+1).(x-2)=0`

`(3x+1).[2.(3x+1)-(x-2)]=0`

`(3x+1).(6x+2-x+2)=0`

`(3x+1).(5x+4)=0`

`3x+1=0` hoặc `5x+4=0`

`3x=-1` hoặc `5x=-4`

`x=-1/3` hoặc `x=-4/5`

Vậy `S={-1/3;-4/5}`

`e)27x^{2}.(x+3)-12.(x^{2}+3x)=0`

`27x^{2}.(x+3)-12.x.(x+3)=0`

`(x+3).(27x^{2}-12x)=0`

`3x.(9x-4).(x+3)=0`

`3x=0` hoặc `9x-4=0` hoặc `x+3=0`

`x=0` hoặc `x=4/9` hoặc `x=-3`

Vậy `S={0;-3;4/9}`

`f)16x^{2}-8x+1=4.(x+3).(4x-1)`

`(4x)^{2}-2.4x.1+1^{2}=(4x-1).(4x+12)`

`(4x-1)^{2}-(4x-1).(4x+12)=0`

`(4x-1).[(4x-1)-(4x+12)]=0`

`(4x-1).(4x-1-4x-12)=0`

`(4x-1).(-13)=0`

`4x-1=0`

`4x=1`

`x=1/4`

Vậy `S={1/4}`