Solve the following equation by factorization:

2x² - 7x = 39

Given,

⇒ 2x² - 7x = 39

⇒ 2x² - 7x - 39 = 0

⇒ 2x² + 6x - 13x - 39 = 0

⇒ 2x(x + 3) - 13(x + 3) = 0

⇒ (x + 3)(2x - 13) = 0

⇒ x + 3 = 0 or 2x - 13 = 0      [Using Zero-product rule]

⇒ x = -3 or 2x = 13

⇒ x = -3 or x = $\dfrac{13}{2}$.

Hence, x = $\Big{\dfrac{13}{2}, -3\Big}$.