Question 760409
Given:
(1) (x-3)/5 - (x+3)/2 = 6
Multiply both sides of (1) by 10 and get
(2) 10*(x-3)/5 - 10*(x+3)/2 = 10*6 or
(3)  2*(x-3) - 5*(x+3) = 60 or 
(4)  2*x -6 - 5*x - 15 = 60 or
(5)  -3*x - 21 = 60 or 
(6)  -3*x = 81 or 
(7)  x = -27
Let's check this using (1). 
Is ((-27-3)/5 - (-27+3)/2 = 6)?
Is (-30/5 - (-24/2) = 6)?
Is (-6 + 12 = 6)?
Is (6 = 6)? Yes
Answer: The solution to the given equation is x = -27.
Comment: The most common error is to have +15 in (4).