`1)`

`(x+7)^2-x(x-3)=12`

`x^2+14x+49-x^2+3x=12`

`11x+49=12`

`11x=-37`

`x=-37/11`

Vậy `x=-37/11`

`2)`

`(2x+3)^2-4x^2=10`

`4x^2+12x+9-4x^2=10`

`12x+9=10`

`12x=1`

`x=1/12`

Vậy `x=1/12`

`3)`

`(x+2)^2-(x-2)(x+1)=3`

`x^2+4x+4-(x^2+x-2x-2)=3`

`x^2+4x+4-x^2+x+2=3`

`5x+6=3`

`5x=-3`

`x=-3/5`

Vậy `x=-3/5`

`4)`

`27x^2(x+1)-(3x+1)^3=-8`

`27x^3+27x^2-(27x^3+27x^2+9x+1)=-8`

`27x^3+27x^2-27x^3-27x^2-9x-1=-8`

`-9x-1=-8`

`-9x=-7`

`x=7/9`

Vậy `x=7/9`

`5)`

`(2x+3)^2-4(x-1)^2=0`

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

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

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

`5(4x+1)=0`

`4x+1=0`

`4x=-1`

`x=-1/4`

Vậy `x=-1/4`

`6)`

`(x+1)(x^2-x+1)-x(x^2-2)=4`

`x^3+1-x^3+2x=4`

`2x+1=4`

`2x=3`

`x=3/2`

Vậy `x=3/2`