To solve this proportion, we can cross multiply:

(x+1)(3x+2) = (x-4)(3x+1)

Expanding both sides:

3x^2 + 2x + 3x + 2 = 3x^2 + x - 12x - 4

Simplifying:

3x^2 + 5x + 2 = 3x^2 - 11x - 4

Subtracting 3x^2 from both sides:

5x + 2 = -11x - 4

Adding 11x to both sides:

16x + 2 = -4

Subtracting 2 from both sides:

16x = -6

Dividing by 16:

x = -6/16

Simplifying:

x = -3/8

So, the solution for the proportion is x = -3/8.