Ta có :
$(x+2).(x+3).(x+4).(x+5)-24=0$
$⇔[(x+2).(x+5)].[(x+3).(x+4)] -24 =0$
$⇔(x^2+7x+10).(x^2+7x+12)-24=0$
$⇔(x^2+7x+10)^2 + 2.(x^2+7x+10)+1-25=0$
$⇔(x^2+7x+11)^2-5^2=0$
$⇔(x^2+7x+6).(x^2+7x+16) = 0 $
$⇔x^2+7x+6=0$
( Do $x^2+7x+16 = (x+\dfrac{7}{2})^2 + \dfrac{15}{4} > 0 $ )
$⇔(x+1).(x+6)=0$
$⇔x=-1,x=-6$