Solve the following equation by factorization:

12x² + 29x + 14 = 0

Given,

⇒ 12x² + 29x + 14 = 0

⇒ 12x² + 21x + 8x + 14 = 0

⇒ 3x(4x + 7) + 2(4x + 7) = 0

⇒ (4x + 7)(3x + 2) = 0

⇒ 4x + 7 = 0 or 3x + 2 = 0      [Using Zero-product rule]

⇒ 4x = -7 or 3x = -2

⇒ x = $\dfrac{-7}{4}$ or x = $\dfrac{-2}{3}$.

Hence, x = $\Big{\dfrac{-7}{4}, \dfrac{-2}{3}\Big}$.