Let's first simplify the equation by squaring both sides:

(x-2)^2(x+sqrt(x-4)) = x^2 - x + 4

Expanding the left side:

(x^2 - 4x + 4)(x + sqrt(x-4)) = x^2 - x + 4

Now expand further:

x^3 - 4x^2 + 4x + x*sqrt(x-4) - 4x - 4sqrt(x-4) + 4 = x^2 - x + 4

Now simplify the equation:

x^3 - 4x^2 + x*sqrt(x-4) - 8sqrt(x-4) = 2

This is the simplified form of the equation.