$ x^4 -x^3 -12x^2-7x+5 =0$
⇔$ ( x^4 -3x^3-5x^2 ) +( 2x^3-6x^2-10x) -( x^2-3x-5 )=0 $
⇔$ x^2 (x^2-3x-5) + 2x(x^2-3x-5) -(x^2-3x-5) = 0$
⇔$ (x^2+2x-1)(x^2-3x-5)= 0$
⇒\(\left[ \begin{array}{l}x^2+2x-1=0\\x^2-3x-5=0\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=-1+-\sqrt[]{2}\\x=(3+-\sqrt[]{29})/2\end{array} \right.\)