Use the substitution 2x + 3 = y to solve for x, if 4(2x + 3)² - (2x + 3) - 14 = 0.

Substituting, 2x + 3 = y in 4(2x + 3)² - (2x + 3) - 14 = 0 we get,

⇒ 4y² - y - 14 = 0

⇒ 4y² - 8y + 7y - 14 = 0

⇒ 4y(y - 2) + 7(y - 2) = 0

⇒ (4y + 7)(y - 2) = 0

⇒ 4y + 7 = 0 or y - 2 = 0

⇒ 4y = -7 or y = 2

⇒ y = $-\dfrac{7}{4}$ or y = 2.

∴ 2x + 3 = $-\dfrac{7}{4}$ or 2x + 3 = 2

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

⇒ 2x = $\dfrac{-7 - 12}{4}$ or 2x = -1

⇒ 2x = $-\dfrac{19}{4} \text{ or } x = -\dfrac{1}{2}$

⇒ x = $-\dfrac{19}{8} \text{ or } x = -\dfrac{1}{2}$

Hence, x = $-\dfrac{19}{8} \text{ or } x = -\dfrac{1}{2}$.