Solve the following equation by factorization:

6x(3x - 7) = 7(7 - 3x)

Given,

⇒ 6x(3x - 7) = 7(7 - 3x)

⇒ 18x² - 42x = 49 - 21x

⇒ 18x² - 42x + 21x - 49 = 0

⇒ 6x(3x - 7) + 7(3x - 7) = 0

⇒ (3x - 7)(6x + 7) = 0

⇒ (3x - 7) = 0 or (6x + 7) = 0      [Using Zero-product rule]

⇒ 3x = 7 or 6x = -7

⇒ x = $\dfrac{7}{3}$ or x = $\dfrac{-7}{6}$.

Hence, x = $\Big{\dfrac{7}{3}, \dfrac{-7}{6}\Big}$.