Solve the following equation by factorization:

10x - $\dfrac{1}{x}$ = 3

Given,

$\Rightarrow 10x - \dfrac{1}{x} = 3 \\[1em] \Rightarrow \dfrac{10x^2 - 1}{x} = 3 \\[1em] \Rightarrow 10x^2 - 1 = 3x \\[1em] \Rightarrow 10x^2 - 3x - 1 = 0 \\[1em] \Rightarrow 10x^2 - 5x + 2x - 1 = 0 \\[1em] \Rightarrow 5x(2x - 1) + 1(2x - 1) = 0 \\[1em] \Rightarrow (5x + 1)(2x - 1) = 0.$

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

⇒ 5x = -1 or 2x = 1

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

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