To solve this inequality, we need to determine the intervals where the expression is greater than or equal to zero.

First, let's find the critical points by setting each factor equal to zero and solving for x:

1) (x-8) = 0
x = 8

2) (x+10) = 0
x = -10

3) (x+3) = 0
x = -3

Now, we can create a number line and test the intervals created by the critical points:

<---(-10)---(-3)---(8)--->

1) Test between -∞ and -10, let's say x = -11:
(-11-8)(-11+10)(-11+3) = (-19)(-1)(-8) = 152
Since the result is positive, this interval is a solution.

2) Test between -10 and -3, let's say x = -5:
(-5-8)(-5+10)(-5+3) = (-13)(5)(-2) = 130
Since the result is negative, this interval is not a solution.

3) Test between -3 and 8, let's say x = 0:
(0-8)(0+10)(0+3) = (-8)(10)(3) = -240
Since the result is negative, this interval is not a solution.

4) Test between 8 and +∞, let's say x = 9:
(9-8)(9+10)(9+3) = (1)(19)(12) = 228
Since the result is positive, this interval is a solution.

Therefore, the solution to the inequality (x-8)(x+10)(x+3) ≥ 0 is x ≤ -10 or -3 ≤ x ≤ 8.