Answer
$(-infinity, -5] U [-2, 6]$
Work Step by Step
$(x+5)(x-6)(x+2) <=0$
$x+5=0$
$x+5-5=0-5$
$x=-5$
$x-6=0$
$x-6+6=0+6$
$x=6$
$x+2=0$
$x+2-2=0-2$
$x=-2$
Four regions to test: $(-∞, -5]$, $[-5, -2]$, $[-2, 6]$, $[6, ∞)$
Let $x=-10$, $x=-3$, $x=0$, $x=10$
$x=-10$
$(x+5)(x-6)(x+2) <=0$
$(-10+5)(-10-6)(-10+2) <=0$
$-5*-16*-8 <=0$
$-640 <=0$ (true)
$x=-3$
$(x+5)(x-6)(x+2) <=0$
$(-3+5)(-3-6)(-3+2) <=0$
$2*-9*-1 <=0$
$2*9 <=0$
$18 <=0$ (false)
$x=0$
$(x+5)(x-6)(x+2) <=0$
$(0+5)(0-6)(0+2) <=0$
$5*-6*2 <=0$
$-60 <=0$ (true)
$x=10$
$(x+5)(x-6)(x+2) <=0$
$(10+5)(10-6)(10+2) <=0$
$15*4*12 <=0$
$720 <=0$ (false)