Equations reducible to the 2nd or 3rd degree;

Got it !

 $6x^3-7x^2+7x+6=0$      Group 2 to 2! $S =\{-1;\frac{2}{3};3\}$ $2x^3+7x^2+7x+2 = 0$      Group 2 to 2! $S =\{-1;-\frac{1}{2};-2\}$ $x^4-x^3-x+1= 0$ $(x-1)(x^3-1)=0 \;\; ; \;\; (x-1)^2(x^2+x+1) =0 \;\; ; \;\; S =\{ 1 \}$ $x^4-5x^3+5x-1= 0$ $(x^2-1)(x^2+1)-5x(x^2-1)=0 \;\; ; \;\; S =\{1;-1;\frac{5+ \sqrt{21}}{2};\frac{5- \sqrt{21}}{2}\}$ $x^3-31x^2+31x-5= 0$ $S =\{1;\frac{1}{5};5\}$