To expand the expression, we can use the distributive property:

(4x - 3)(3x + 4) + (2x - 3)(3x + 1)
= 4x(3x) + 4x(4) - 3(3x) - 3(4) + 2x(3x) + 2x(1) - 3(3x) - 3(1)
= 12x^2 + 16x - 9x - 12 + 6x^2 + 2x - 9x - 3
= 12x^2 + 6x^2 + 16x - 9x - 9x + 2x + 2 - 12 - 3
= 18x^2 - 10x - 13

Therefore, (4x - 3)(3x + 4) + (2x - 3)(3x + 1) simplifies to 18x^2 - 10x - 13.