To solve the inequalities:

1) (x+3)(x-0.5) < 0
Expanding the terms:
x^2 + 3x - 0.5x - 1.5 < 0
x^2 + 2.5x - 1.5 < 0
(x+3)(x-0.5) = 0
x = -3 or x = 0.5

Putting x = -4 into the inequality:
(-4+3)(-4-0.5) = (-1)(-4.5) = 4.5 > 0
So the solution is -3 < x < 0.5

2) (x-3)(5x-6)(x+6) < 0
Expanding the terms:
5x^3 - 30x^2 + 6x^2 - 36x - 15x + 90 < 0
5x^3 - 30x^2 + 6x^2 - 51x + 90 < 0
5x^3 - 24x^2 - 51x + 90 < 0
(x-3)(5x-6)(x+6) = 0
x = 3, x = 6/5 or x = -6

Putting x = -7 into the inequality:
(-7-3)(-35-6)(-1) = (-10)(-41)(-1) = 410 > 0
Putting x = -5/2 into the inequality:
(-5/2-3)(-25/2-6)(3/2) = (-11/2)(-37/2)(3/2) = 203.25 > 0
So the solution is -6 < x < 3 or 6/5 < x < ∞