Solve the following equation by factorization:

x(6x - 11) = 35

Given,

⇒ x(6x - 11) = 35

⇒ 6x² - 11x - 35 = 0

⇒ 6x² + 10x - 21x - 35 = 0

⇒ 2x(3x + 5) - 7(3x + 5) = 0

⇒ (3x + 5)(2x - 7) = 0

⇒ (3x + 5) = 0 or (2x - 7) = 0      [Using Zero-product rule]

⇒ 3x = -5 or 2x = 7

⇒ x = $\dfrac{-5}{3}$ or x = $\dfrac{7}{2}$.

Hence, x = $\Big{\dfrac{-5}{3}, \dfrac{7}{2}\Big}$.