Solve the following equation by factorization:

5x - $\dfrac{35}{x}$ = 18

Given,

$\Rightarrow 5x - \dfrac{35}{x} = 18 \\[1em] \Rightarrow \dfrac{5x^2 - 35}{x} = 18 \\[1em] \Rightarrow 5x^2 - 35 = 18x \\[1em] \Rightarrow 5x^2 - 18x - 35 = 0 \\[1em] \Rightarrow 5x^2 - 25x + 7x - 35 = 0 \\[1em] \Rightarrow 5x(x - 5) + 7(x - 5) = 0 \\[1em] \Rightarrow (5x + 7)(x - 5) = 0.$

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

⇒ 5x = -7 or x = 5

⇒ x = $\dfrac{-7}{5}$ or x = 5.

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