\begin{array}{rcl}-x^2(6(x^2+1/x^2)-35(x+1/x)+62)&=&-x^2(6(t^2-2)-35t+62)-x^2(6t^2-35t+50)
\vspace{0.5em}\\ &=&
-6x^2(t^2-(35/6)t+25/3)
\vspace{0.5em}\\ &=&
-6x^2(t-5/2)(t-10/3)
\vspace{0.5em}\\ &=&
-x^2(2t-5)(3t-10)
\vspace{0.5em}\\ &=&
-(2tx-5x)(3tx-10x)
\vspace{0.5em}\\ &=&
-(2(x^2+1)-5x)(3(x^2+1)-10x)
\vspace{0.5em}\\ &=&
-(2x^2-5x+2)(3x^2-10x+3)
\vspace{0.5em}\\ &=&
(x-2)(2x-1)(x+3)(3x+1)
\end{array}