Verified answer

(x + 2)² =(x - 4)²

(x + 2)² - (x - 4)² = 0

(x + 2 - x + 4)(x + 2 + x - 4) = 0

6(2x - 2) = 0

6 ≠ 0      ⇒  2x - 2 = 0      2x = 2     x = 1