To solve each of these equations, we need to apply the distributive property and combine like terms on both sides of the equation.

1) 4x^2 - 3x = 3(12 - x)
4x^2 - 3x = 36 - 3x
4x^2 = 36
x^2 = 9
x = ±3

2) x^2 - 3x = 2(12 - x) - x
x^2 - 3x = 24 - 2x - x
x^2 + 3x - 24 = 0
(x + 8)(x - 3) = 0
x = -8 or x = 3

3) -x^2 + 6x = 2(12 + 2x) + 2x
-x^2 + 6x = 24 + 4x + 2x
-x^2 = 24x
x^2 = -24x
x = 0 or x = -24

Please double-check the calculations to ensure accuracy.