Let's simplify the left-hand side of the equation first:
7[x+4] - 2[(x-3(5+x)] = 2/3 [x-6]
7x + 28 - 2[x - 15 - 3x] = 2/3 [x-6] // Distribute the negative sign
7x + 28 - 2x + 30 + 6x = 2/3 [x-6] // Simplify the terms inside the parentheses
11x + 58 = 2/3 [x-6] // Simplify the terms on the left-hand side
Multiplying both sides by 3 gives:
33x + 174 = 2(x-6) // Distribute 2/3 on the right-hand side
33x + 174 = 2x - 12
Subtracting 2x and 174 from both sides gives:
31x = -186
Dividing both sides by 31 gives:
x = -6
Therefore, the solution to the equation is x = -6