4/5(7-3x) - 1/3(x+3) = 2/5(x-6)

Expanding the left side:
28/5 - 12/5x - 1/3x - 1 = 2/5x - 12/5

Combine like terms:
28/5 - 12/5x - 1/3x - 1 = 2/5x - 12/5
28/5 - 12/5x - 1/3x - 1 + 12/5 = 2/5x
28/5 - 12/5x - 1/3x - 1 + 60/15 = 2/5x
28/5 - 12/5x - 5/15x - 1 + 60/15 = 2/5x
28/5 - 12/5x - 1/3x - 1 + 60/15 = 2/5x

Now simplify and solve for x:
28/5 - 21/15 - 1 = 2/5x
28/5 - 7/15 - 1 = 2/5x
28/5 - 7/15 - 15/15 = 2/5x
28/5 - 22/15 = 2/5x
84/15 - 22/15 = 2/5x
62/15 = 2/5x
625 = 215x
310 = 30x
310/30 = x
31/3 = x

Therefore, the solution for the equation is x = 31/3 or x = 10.33.