`(x + 1)^2 . (x + 2) + (x - 1)^2 . (x - 2) = 12` 

`<=> (x^2 + 2x + 1) . (x + 2) + (x^2 - 2x + 1) . (x - 2) = 12` 

`<=> x^3 + 2x^2 + 2x^2 + 4x + x + 2 + x^3 - 2x^2 - 2x^2 + 4x + x - 2 = 12` 

`<=> (x^3 + x^3) + (2x^2 + 2x^2 - 2x^2 - 2x^2) + (4x + 4x + x + x) + (2 - 2) = 12` 

`<=> 2x^3 + 10x - 12 = 0` 

`<=> x^3 + 5x - 6 = 0` 

`<=> (x^3 - 1) + (5x - 5) = 0` 

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

`<=> (x - 1) . (x^2 + x + 6) = 0` 

`<=> x - 1 = 0; x^2 + x + 6 = 0` 

`<=> x = 1; x^2 + 2 . x . 1/2 + 1/4 + 23/4 = 0` 

`<=> x = 1; (x + 1/2)^2 = (-23)/4 (loại)` 

`Vậy: S = {1}`