First we need to expand both sides of the equation:

(3x-1)^2 = (3x-1)(3x-1) = 9x^2 - 6x + 1

(4x+5)^2 = (4x+5)(4x+5) = 16x^2 + 40x + 25

(5x-7)^2 = (5x-7)(5x-7) = 25x^2 - 70x + 49

Now we can substitute these back into the equation:

(9x^2 - 6x + 1) + (16x^2 + 40x + 25) = 25x^2 - 70x + 49

Simplify the equation:

25x^2 - 6x + 1 + 16x^2 + 40x + 25 = 25x^2 - 70x + 49

41x^2 + 34x + 26 = 25x^2 - 70x + 49

Now, let's simplify further by combining like terms:

41x^2 + 34x + 26 - 25x^2 + 70x -49 = 0

16x^2 + 104x - 23 = 0

Since this is a quadratic equation, we can try to solve it by factoring, completing the square, or using the quadratic formula.