To solve 2(2x - 3)² = 32, we can start by dividing both sides of the equation by 2:
(2x - 3)² = 16
Next, we take the square root of both sides of the equation:
2x - 3 = ±4
Now we solve for x by adding 3 to both sides of each equation:
2x = 7 or 2x = -1
Finally, we divide both sides of each equation by 2 to get:
x = 7/2 or x = -1/2
Therefore, the solutions to the equation 2(2x - 3)² = 32 are x = 7/2 or x = -1/2.