Let's first simplify both sides of the inequality:

Left side: (5x+1)(3x-1) = 15x^2 + 5x - 3x - 1 = 15x^2 + 2x - 1

Right side: (4x-1)(x+2) = 4x^2 + 8x - x - 2 = 4x^2 + 7x - 2

Now, our inequality becomes:

15x^2 + 2x - 1 > 4x^2 + 7x - 2

Rearranging terms, we get:

15x^2 + 2x - 1 - 4x^2 - 7x + 2 > 0

Simplifying further, we get:

11x^2 - 5x + 1 > 0

Now, in order to solve this quadratic inequality, we can use different methods like graphing, factoring or using the discriminant.

After solving, we find the solution to the inequality is:

x < 5/22 or x > 1/11

Therefore, the inequality (5x+1)(3x-1)>(4x-1)(x+2) holds when x is less than 5/22 or greater than 1/11.