To solve this equation, we first need to simplify both sides of the equation.

Starting with the left side:
3(x-7) - (9-2x)
= 3x - 21 - 9 + 2x
= 5x - 30

Now simplifying the right side:
2(12-x) - (x-10)
= 24 - 2x - x + 10
= 34 - 3x

So the equation now becomes:
5x - 30 = 34 - 3x

Now, we need to solve for x:
5x + 3x = 34 + 30
8x = 64
x = 8

Therefore, the solution to the equation is x = 8.