Solve the following equation by factorization:

3a²x² + 8abx + 4b² = 0, a ≠ 0

Given,

⇒ 3a²x² + 8abx + 4b² = 0

⇒ 3a²x² + 6abx + 2abx + 4b² = 0

⇒ 3ax(ax + 2b) + 2b(ax + 2b) = 0

⇒ (3ax + 2b)(ax + 2b) = 0

⇒ (3ax + 2b) = 0 or (ax + 2b) = 0      [Using Zero-product rule]

⇒ 3ax = -2b or ax = -2b

⇒ x = $-\dfrac{2b}{3a}$ or x = $-\dfrac{2b}{a}$.

Hence, x = $\Big{-\dfrac{2b}{a}, -\dfrac{2b}{3a}\Big}$.