Answer
$(-∞, -5]$ U $[-2, 6]$
Work Step by Step
$(x+5)(x-6)(x+2) \le 0$
$x+5=0$
$x+5-5=0-5$
$x=-5$
$x-6=0$
$x-6+6=0+6$
$x=6$
$x+2=0$
$x+2-2=0-2$
$x=-2$
Four regions to test: $(-∞, -5]$, $[-5, -2]$, $[-2, 6]$, $[6,∞)$
Let $x=-6$, $x=-3$, $x=0$, $x=7$
$x=-6$
$(x+5)(x-6)(x+2) \le 0$
$(-6+5)(-6-6)(-6+2) \le 0$
$-1*-12*-4 \le 0$
$-48 \le 0$ (true)
$x=-3$
$(x+5)(x-6)(x+2) \le 0$
$(-3+5)(-3-6)(-3+2) \le 0$
$2*-9*-1 \le 0$
$18 \le 0$ (false)
$x=0$
$(x+5)(x-6)(x+2) \le 0$
$(0+5)(0-6)(0+2) \le 0$
$5*-6*2 \le 0$
$-60 \le 0$ (true)
$x=7$
$(x+5)(x-6)(x+2) \le 0$
$(7+5)(7-6)(7+2) \le 0$
$12*1*9 \le 0$
$108 \le 0$ (false)
