we have the inequality
(x+2)(x-1)(x+4) < 0
Remember that
the zeros of this expression are
x=-2
x=1
x=-4
therefore
we have the intervals
(-infinite,-4) (-4,-2) (-2,1) (1, infinite)
Evaluate each interval
so
(x+2)(x-1)(x+4) < 0
(-infinite,-4)
For x=-10
(-10+2)(-10-1)(-10+4) < 0
((-8)(-11)(-6) <0
-528 < 0 ----> is true
that means
the interval (-infinite,-4) is part of the solution
Interval (-4,-2)
For x=-3
substitute
(-3+2)(-3-1)(-3+4) < 0
(-1)(-4)(1) < 0
4 < 0 ----> is not true
that means
interval (-4,-2) is not a solution
Interval (-2,1)
For x=0
substitute
(0+2)(0-1)(0+4) < 0
(2)(-1)(4) < 0
-8 < 0 ----> is true
the interval (-2,1) is part of the solution
Interval (1, infinite)
For x=2
substitute
(2+2)(2-1)(2+4) < 0
(4)(1)(6) < 0
24 < 0 ----> is not true
therefore
the solution for the inequality is
(-infinite,-4) U (-2,1)