a) $x^2+5x+6=0$
$⇔x^2+2x+3x+6=0$
$⇔(x+2)(x+3)=0$
$⇔ \left[ \begin{array}{l}x+2=0\\x+3=0\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=-2\\x=-3\end{array} \right.$
b) $x^2+x-12=0$
$⇔x^2+4x-3x-12=0$
$⇔(x+4)(x-3)=0$
$⇔ \left[ \begin{array}{l}x+4=0\\x-3=0\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=-4\\x=3\end{array} \right.$
c) $x^4+2x^3-2x^2+2x-3=0$
$⇔x^4-x^3+3x^3-3x^2+x^2-x+3x-3=0$
$⇔(x-1)(x^3+3x^2+x+3)=0$
$⇔(x-1)[x^2.(x+3)+(x+3)]=0$
$⇔(x-1)(x+3)(x^2+1)=0$
$⇔ \left[ \begin{array}{l}x-1=0\\x+3=0\\x^2+1=0\end{array} \right.$
$⇔ \left[ \begin{array}{l}x=1\\x=-3\end{array} \right.$ ( Do $x^2+1 > 0 $)
