To solve this inequality, we need to find the values of n that make the expression (2n+6) divisible by (2n-1).

First, let's rewrite the expression as a division:

(2n+6) ÷ (2n-1)

To find the values of n that make this expression divisible, we need to find the values of n that make the remainder of the division equal to zero.

We can use long division to divide (2n+6) by (2n-1):

2
___________
(2n-1) | 2n + 6

When we divide 2n by 2n, we get 1. Then, we multiply (2n-1) by 1 to get 2n-1. Subtracting this from 2n+6, we get 7. We bring down the 6 and divide 7 by (2n-1) again:

2 + 7/(2n-1)
___________
(2n-1) | 2n + 6 + 7/(2n-1)

We can see that the remainder is 7/(2n-1). For the expression to be divisible, the remainder must be zero. Therefore, we need to solve the equation:

7/(2n-1) = 0

However, this equation has no solution because dividing any number by zero is undefined.

Therefore, there are no values of n that make the expression (2n+6) divisible by (2n-1).