Expanding the left side of the equation:

(2x + 5)² = (2x + 5)(2x + 5) = 4x² + 20x + 25
(5x - 3)² = (5x - 3)(5x - 3) = 25x² - 30x + 9

Adding them together:

4x² + 20x + 25 + 25x² - 30x + 9 = 75 + 2x

Combining like terms:

29x² - 10x + 34 = 75 + 2x

Rearranging the equation:

29x² - 10x + 34 - 75 - 2x = 0
29x² - 12x - 41 = 0

Therefore, the solution for x cannot be simplified further and is given by:

x = [-(-12) ± √((-12)² - 4(29)(-41))] / 2(29)
x = [12 ± √(144 + 4732)] / 58
x = [12 ± √4876] / 58
x ≈ [12 ± 69.824] / 58
x ≈ [81.824 or -57.824] / 58
x ≈ 1.41 or -0.998

Therefore, the possible values for x are approximately 1.41 and -0.998.