Đáp án+Giải thích các bước giải:

 `1)4x.(x-5)-(x-1).(4x-3)=5`

`4x^{2}-20x-(4x^{2}-3x-4x+3)=5`

`4x^{2}-20x-4x^{2}-(-7x)-3=5`

`-20x+7x=5+3`

`-13x=8`

`x=-8/13`

Vậy `x=-8/13`

`2)(3x-4).(x-2)=3x.(x-9)-3`

`3x^{2}-6x-4x+8=3x^{2}-27x-3`

`3x^{2}-10x+8-3x^{2}+27x+3=0`

`17x+11=0`

`17x=-11`

`x=-11/17`

Vậy `x=-11/17`

`3)(x-5).(x-4)-(x+1).(x-2)=7`

`x^{2}-4x-5x+20-(x^{2}-2x+x-2)=7`

`x^{2}-9x+20-x^{2}-(-x)+2=7`

`-9x+x=7-20-2`

`-8x=-15`

`x=15/8`

Vậy `x=15/8`

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

`5x^{2}-15x=5x^{2}-x-10x+2-5`

`5x^{2}-15x-5x^{2}+x+10x=-3`

`-4x=-3`

`x=3/4`

Vậy `x=3/4`

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

`(x-5).(x-1)-(x-1).(x-2)=0`

`(x-1).[(x-5)-(x-2)]=0`

`(x-1).(x-5-x+2)=0`

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

`x-1=0`

`x=1`

Vậy `x=1`

`6)6.(x-3).(x-4)-6x.(x-2)=4`

`(6x-18).(x-4)-6x^{2}+12x=4`

`6x^{2}-24x-18x+72-6x^{2}+12x=4`

`-30x=4-72`

`-30x=-68`

`x=34/15`

Vậy `x=34/15`

`7)-(x+3).(x-4)+(x-1).(x+1)=10`

`-(x^{2}-4x+3x-12)+x^{2}-1^{2}=10`

`-x^{2}-(-x)+12+x^{2}-1=10`

`x=10-12+1`

`x=-1`

Vậy `x=-1`

`8)(2x-1).(x-2)-(x+3).(2x-7)=3`

`2x^{2}-4x-x+2-(2x^{2}-7x+6x-21)=3`

`2x^{2}-5x+2-2x^{2}-(-x)+21=3`

`-5x+x=3-2-21`

`-4x=-20`

`x=5`

Vậy `x=5`

`9)(x-5).(-x+4)-(x-1).(x+3)=-2x^{2}`

`-x^{2}+4x+5x-20-(x^{2}+3x-x-3)=-2x^{2}`

`-x^{2}+9x-20-x^{2}-2x+3=-2x^{2}`

`-2x^{2}+7x-(20-3)=-2x^{2}`

`-2x^{2}+2x^{2}+7x-17=0`

`7x=17`

`x=17/7`

Vậy `x=17/7`

`10)(4x+1).(x-3)-(x-7).(4x-1)=15`

`4x^{2}-12x+x-3-(4x^{2}-x-28x+7)=15`

`4x^{2}-11x-3-4x^{2}-(-29x)-7=15`

`-11x+29x=15+3+7`

`18x=25`

`x=25/18`

Vậy `x=25/18`