To solve this equation, we can use the double angle formula for sine and cosine:

Convert sin(2x) in terms of cos(2x):
sin(2x) = 2sin(x)cos(x)

Convert cos(2x) in terms of cos(x):
cos(2x) = 2cos²(x) - 1

Now, we can substitute these values in the given equation:

2sin(x)cos(x) - 2√3cos²(x) - 4sin(x) + 4√3cos(x) = 0

Factor out common terms:
2sin(x)cos(x) - 4sin(x) - 2√3cos²(x) + 4√3cos(x) = 0

Rearrange terms:
2sin(x)(cos(x) - 2) - 2√3cos(x)(cos(x) - 2) = 0

Factor out common terms:
(2sin(x) - 2√3cos(x))(cos(x) - 2) = 0

Now, we can set each factor equal to zero and solve for x:

2sin(x) - 2√3cos(x) = 0
Divide by 2:
sin(x) = √3cos(x)

Divide by cos(x) on both sides:
tan(x) = √3
x = π/3 + nπ, where n is an integer

cos(x) - 2 = 0
cos(x) = 2
This is not valid as the range of cosine function is [-1, 1]

Therefore, the solution to the given equation is x = π/3 + nπ, where n is an integer.