Expanding the left side of the equation, we get:

(2x^2 - x + 1)^2 - 4x^2 + 2x - 1
= (4x^4 - 2x^3 + 2x^2 - 2x^3 + x^2 - x + 2x^2 - x + 1) - 4x^2 + 2x - 1
= 4x^4 - 4x^3 + 5x^2 - 2x + 1 - 4x^2 + 2x - 1
= 4x^4 - 4x^3 + x^2
= x^2(4x^2 - 4x + 1)
= x^2(2x - 1)^2

Setting the expression equal to zero:

x^2(2x - 1)^2 = 0

This equation is true when x = 0 or when 2x - 1 = 0, which simplifies to x = 1/2.

Therefore, the solutions to the equation (2x^2 - x + 1)^2 - 4x^2 + 2x - 1 = 0 are x = 0 and x = 1/2.