Solve the following equation by factorization:

10x² = 9x + 7

Given,

⇒ 10x² = 9x + 7

⇒ 10x² - 9x - 7 = 0

⇒ 10x² + 5x - 14x - 7 = 0

⇒ 5x(2x + 1) - 7(2x + 1) = 0

⇒ (2x + 1)(5x - 7) = 0

⇒ (2x + 1) = 0 or (5x - 7) = 0      [Using Zero-product rule]

⇒ 2x = -1 or 5x = 7

⇒ x = $-\dfrac{1}{2}$ or x = $\dfrac{7}{5}$.

Hence, x = $\Big{-\dfrac{1}{2}, \dfrac{7}{5}\Big}$.