Let's simplify the equation step by step:

First, let's simplify the left side of the equation:
7(3x - x) - 3(x - 4)
= 7(2x) - 3(x - 4)
= 14x - 3x + 12
= 11x + 12

Now, let's simplify the right side of the equation:
5(3 + 2x) - 2(-3 - 2x)
= 5(3) + 5(2x) + 2(3) + 2(2x)
= 15 + 10x + 6 + 4x
= 10x + 21

Now we can set the left side equal to the right side:
11x + 12 = 10x + 21

Subtract 10x from both sides:
11x - 10x + 12 = 21
x + 12 = 21

Subtract 12 from both sides:
x = 9

Therefore, the solution to the equation is x = 9.