To find the intervals where the inequality is true, we will first find the critical points by setting each factor equal to zero:

x^2 - 6x + 10 = 0
This is a quadratic equation that does not have real roots, so this factor does not contribute to the critical points.

x - 3 = 0
x = 3

x^2 - 9 = 0
x^2 = 9
x = ±3

So, the critical points are x = -3, x = 3, and x=-3.

Next, we will test each interval created by the critical points (i.e., (-∞, -3), (-3, 3), (3, ∞)) by plugging in test points into the original inequality:

Test x = -4 (in (-∞, -3)):
(-4)^2 - 6*(-4) + 10 < 0
16 + 24 + 10 < 0
50 < 0
This is false, so (-∞, -3) is not part of the solution.

Test x = 0 (in (-3, 3)):
(0)^2 - 6*(0) + 10 > 0
10 > 0
This is true, so (-3, 3) is part of the solution.

Test x = 4 (in (3, ∞)):
(4)^2 - 6*(4) + 10 > 0
16 - 24 + 10 > 0
2 > 0
This is true, so (3, ∞) is part of the solution.

Therefore, the solution to the inequality (x^2-6x+10)(x-3)(x^2-9) > 0 is x ∈ (-3, 3) U (3, ∞).