Đáp án+Giải thích các bước giải:

 `a)(2x+1)^{2}-(x+7).(x-7)-3.(x+2)^{2}=5`

`(2x)^{2}+2.2x.1+1^{2}-(x^{2}-7^{2})-3.(x^{2}+2.x.2+2^{2})=5`

`4x^{2}+4x+1-x^{2}+49-3x^{2}-12x-12=5`

`(4x^{2}-x^{2}-3x^{2})+(4x-12x)+(1-12+49)=5`

`-8x+38-5=0`

`-8x+33=0`

`-8x=-33`

`x=33/8`

Vậy `x=33/8`

`b)(3-4x)^{2}-(5-x).(4x+2)-3.(2x+1).(2x-1)=7`

`3^{2}-2.3.4x+(4x)^{2}-(20x+10-4x^{2}-2x)-3.[(2x)^{2}-1^{2}]=7`

`9-24x+16x^{2}-(-4x^{2}+18x+10)-3.(4x^{2}-1))=7`

`16x^{2}-24x+9+4x^{2}-18x-10-12x^{2}+3=7`

`8x^{2}-42x-5=0`

`8.(x^{2}-21/4x-5/8)=0`

`x^{2}-2.x. 21/8+(21/8)^{2}-5/8-(21/8)^{2}=0`

`(x-21/8)^{2}-\frac{481}{64}=0`

`(x-21/8)^{2}=(\pm\frac{\sqrt{481}}{8})^{2}`

`x-21/8=\frac{\sqrt{481}}{8}` hoặc `x-21/8=-\frac{\sqrt{481}}{8}`

`x=\frac{21+\sqrt{481}}{8}` hoặc `x=\frac{21-\sqrt{481}}{8}`

Vậy `x\in{\frac{21+\sqrt{481}}{8};\frac{21-\sqrt{481}}{8}}.`

`c)(3x+1)^{2}-(2-3x)^{2}-7.(x+3)=9`

`(3x+1-2+3x).(3x+1+2-3x)-7x-21-9=0`

`(6x-1).3-7x-30=0`

`18x-3-7x-30=0`

`11x-33=0`

`11x=33`

`x=3`

Vậy `x=3`

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

`(3+2x).(3-2x)+3^{2}-2.3.x+x^{2}+(3x-6).(5+x)=4`

`3^{2}-(2x)^{2}+9-6x+x^{2}+(15x+3x^{2}-30-6x)=4`

`9-4x^{2}+x^{2}-6x+9+(3x^{2}+9x-30)=4`

`-3x^{2}-6x+18+3x^{2}+9x-30=4`

`3x-12-4=0`

`3x-16=0`

`3x=16`

`x=16/3`

Vậy `x=16/3`