\(x^3-3x^2-3x-4=0\)
\(\Leftrightarrow x^3-4x^2+x^2-4x+x-4=0\)
\(\Leftrightarrow x^2\left(x-4\right)+x\left(x-4\right)+\left(x-4\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x^2+x+1\right)=0\)
\(\Leftrightarrow x-4=0\) (vì \(x^2+x+1>0\))
\(\Leftrightarrow x=4\)
Vậy \(S=\left\{4\right\}\)