Solve the following equation by factorisation:

4(2x - 3)² - (2x - 3) - 14 = 0

4(2x - 3)² - (2x - 3) - 14 = 0

⇒ 4(4x² + 9 - 12x) - 2x + 3 - 14 = 0

⇒ 16x² + 36 - 48x - 2x - 11 = 0

⇒ 16x² - 50x + 25 = 0

⇒ 16x² - 40x - 10x + 25 = 0

⇒ 8x(2x - 5) - 5(2x - 5) = 0

⇒ (8x - 5)(2x - 5) = 0

⇒ 8x - 5 = 0 or 2x - 5 = 0      [Using Zero-product rule]

⇒ 8x = 5 or 2x = 5

⇒ x = $\dfrac{5}{8}$ or x = $\dfrac{5}{2}$.

Hence, x = $\dfrac{5}{8} \text{ or } x = \dfrac{5}{2}$.