Expand the left side of the equation
4x^2 - 8x + 2 = 1
Subtract 1 from both sides of the equation
4x^2 - 8x + 1 = 0
Factor the left side of the equation to get
(2x - 1) ( 2x - 1) = 0
This means that either 2x-1 = 0 or 2x-1 = 0.
If 2x-1 = 0, then x = 1/2.
If 2x-1 = 0, then x = 1/2.
Therefore, the solutions to the equation 2(x -2)(2x-1) = 1 are x= 1/2 and x = 1/2