Expanding the left side of the inequality:
(3x-4)(7x+5)
= 3x(7x) + 3x(5) - 4(7x) - 4(5)
= 21x^2 + 15x - 28x - 20
= 21x^2 - 13x - 20

Expanding the right side of the inequality:
(3x-4)(7x-5)
= 3x(7x) + 3x(-5) - 4(7x) - 4(-5)
= 21x^2 - 15x - 28x + 20
= 21x^2 - 43x + 20

So, the inequality becomes:
21x^2 - 13x - 20 ≥ 21x^2 - 43x + 20

Now, let's simplify the equation:
21x^2 - 13x - 20 ≥ 21x^2 - 43x + 20
0 ≥ -30x + 40
30x ≥ 40
x ≥ 4/3

Therefore, the solution to the inequality is x ≥ 4/3.