$(1−2 x )(3 x+7)=1−4 x²$
$⇔ 3x+7-6x²-14x-1+4x²=0$
$⇔ -2x²-11x+6=0$
$⇔ -2x²+x-12x+6=0$
$⇔ -x(2x-1)-6(2x-1)=0$
$⇔ (2x-1)(-x-6)=0$
$⇔$ \(\left[ \begin{array}{l}2x-1=0\\-x-6=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}2x=1\\-x=6\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x=0,5\\x=-6\end{array} \right.\)
Vậy $S=\{0,5;-6\}$