To solve the inequality (x+7)(x-6)(x-14) < 0, we need to find the values of x that make the expression less than zero.

First, let's find the critical points by setting each factor equal to zero:
x+7 = 0
x = -7

x-6 = 0
x = 6

x-14 = 0
x = 14

These critical points divide the number line into four intervals: (-∞,-7), (-7, 6), (6, 14), and (14,∞).

Now we test a value in each interval to see if the expression is positive or negative:
For x = -8: (-1)(-14)(-22) > 0, not less than 0
For x = 0: (7)(-6)(-14) < 0
For x = 10: (17)(4)(-4) < 0
For x = 15: (22)(9)(1) > 0, not less than 0

Therefore, the solution to the inequality (x+7)(x-6)(x-14) < 0 is 6 < x < 14.