To solve this equation, first distribute on both sides of the equation:

5(3x-2) = 15x - 10

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

So now the equation becomes:

15x - 10 = x - 3

Next, combine like terms by subtracting x from both sides:

14x - 10 = -3

Add 10 to both sides:

14x = 7

Divide by 14:

x = 7/14 = 1/2

Therefore, the solution to the equation is x = 1/2.