$6x^4+5x^3-38x^2+5x+6=0$
$\to 6x^4-12x^3+17x^3-34x^2-4x^2+8x-3x+6=0$
$\to 6x^3(x-2)+17x^2(x-2)-4x(x-2)-3(x-2)=0$
$\to (x-2)(6x^3+17x^2-4x-3)=0$
$\to (x-2)(6x^3+18x^2-x^2-3x-x-3)=0$
$\to (x-2)[6x^2(x+3)-x(x+3)-(x+3)]=0$
$\to (x+3)(x-2)(6x^2-x-1)=0$
$\to (x+3)(x-2)(6x^2-3x+2x-1)=0$
$\to (x+3)(x-2)[3x(2x-1)+(2x-1)]=0$
$\to (x+3)(x-2)(2x-1)(3x+1)=0$
$\\$ $\to \begin{cases}x+3=0\\x-2=0\\2x-1=0\\3x+1=0\end{cases}$$ \to \begin{cases}x=-3\\x=2\\x=\dfrac{1}{2}\\x=-\dfrac{1}{3}\end{cases}$
Vậy $S={-3;2;\dfrac{1}{2}-\dfrac{1}{3}}$
