Let's first simplify the equation by distributing the coefficients:

5 2 - 5 3x - 4 6 - 4 2x = 28 - x + 2

Now, calculate the products:

10 - 15x - 24 - 8x = 30 - x

Combine like terms:

-15x - 8x - 24 + 10 = 30 - x

-23x - 14 = 30 - x

Now, isolate the variable x:

-23x + x = 30 + 14

-22x = 44

x = -2

Therefore, the solution to the equation 5(2-3x)-4(6+2x)=28-(x-2) is x = -2.