We need to solve the equation: w² + 36 = 12w
⇒ w² - 12w + 36 = 0
⇒ w² - 6w - 6w + 36 = 0 (Breaking 6w such that their product is 9w²)
⇒ w × (w - 6) - 6 × (w - 6) = 0 (Extracting common factors)
⇒ (w - 6) × (w - 6) = 0
⇒ (w - 6)² = 0
⇒ w = 6
Hence, the correct answer is 6 which is the fourth option from the replacement set