Expanding the terms, we get:

(4x+1)(x+5) = 4x^2 + 20x + x + 5 = 4x^2 + 21x + 5

(2x+1)(2x-3) = 4x^2 - 6x + 2x - 3 = 4x^2 - 4x - 3

Substitute these into the equation:

(4x^2 + 21x + 5) - (4x^2 - 4x - 3) = 58

4x^2 + 21x + 5 - 4x^2 + 4x + 3 = 58

Combine like terms:

25x + 8 = 58

Subtract 8 from both sides:

25x = 50

Divide by 25:

x = 2

Therefore, the solution to the equation is x = 2.