Expanding the left side of the equation:

(3x - 5)(2x + 7) = 6x^2 + 21x - 10x - 35
= 6x^2 + 11x - 35

Expanding the right side of the equation:

(3x + 1)(2x - 3) + 4x = 6x^2 - 9x + 2x - 3 + 4x
= 6x^2 - 3x + 1

Equating both sides of the equation:

6x^2 + 11x - 35 = 6x^2 - 3x + 1

To solve for x, we need to simplify the equation:

6x^2 - 6x^2 + 11x + 3x = 1 + 35
14x = 36
x = 36/14
x = 18/7