`(3x+4)(x+1)(6x+7)^2=6`

`12(3x+4)(x+1)(6x+7)^2=6*12`

`(6x+8)(6x+6)(6x+7)^2=12*6`

`[(6x+8)(6x+6)](6x+7)^2=72`

`( 36x^2+84x+48)( 36x^2+84x+49)=72`

Đặt: `36x^2+84x+48=t`

Ta được pt:

`t(t+1)=72`

`t^2+t-72=0`

`t(t-8)+9(t-8)=0`

`(t+9)(t-8)=0`

`t=-9` hoặc `t=8`

`TH1:t=-9`

`->36x^2+84x+48=-9`

`36x^2+84x+57=0`

`12x^2+28x+19=0`

`\Delta=(28)^2-4*12*19=-128<0`

Nên vô nghiệm

`TH2:t=8`

`->36x^2+84x+48=8`

`36x^2+84x+40=0`

`\Delta=84^2-4*36*40=1296`

`->x_1=(-84+\sqrt{1296})/(2*36)=-2/3`

`x_2=(-84-\sqrt{432})/(2*36)=-5/3`

Vậy: `S={-2/3;-5/3}`