Determine whether x = $-\dfrac{1}{3}$ and x = $\dfrac{2}{3}$ are the solutions of the equation 9x² - 3x - 2 = 0.

Given,

⇒ 9x² - 3x - 2 = 0

⇒ 9x² - 6x + 3x - 2 = 0

⇒ 3x(3x - 2) + 1(3x - 2) = 0

⇒ (3x + 1)(3x - 2) = 0

⇒ 3x + 1 = 0 or 3x - 2 = 0      [Using Zero-product rule]

⇒ 3x = -1 or 3x = 2

⇒ x = $\dfrac{-1}{3}$ or x = $\dfrac{2}{3}$.

Hence, $\dfrac{-1}{3}, \dfrac{2}{3}$ are the solutions of the equation 9x² - 3x - 2 = 0.