Solve the following equation by factorisation:

$\dfrac{5}{x - 2} - \dfrac{3}{x + 6} = \dfrac{4}{x}$

Given,

$\Rightarrow \dfrac{5(x + 6) - 3(x - 2)}{(x - 2)(x + 6)} = \dfrac{4}{x} \\[1em] \Rightarrow \dfrac{5x + 30 - 3x + 6}{x^2 + 6x - 2x - 12} = \dfrac{4}{x} \\[1em] \Rightarrow \dfrac{2x + 36}{x^2 + 4x - 12} = \dfrac{4}{x} \\[1em] \Rightarrow x(2x + 36) = 4(x^2 + 4x - 12) \\[1em] \Rightarrow 2x^2 + 36x = 4x^2 + 16x - 48 \\[1em] \Rightarrow 4x^2 - 2x^2 + 16x - 36x - 48 = 0 \\[1em] \Rightarrow 2x^2 - 20x - 48 = 0 \\[1em] \Rightarrow 2(x^2 - 10x - 24) = 0 \\[1em] \Rightarrow x^2 - 10x - 24 = 0 \\[1em] \Rightarrow x^2 - 12x + 2x - 24 = 0 \\[1em] \Rightarrow x(x - 12) + 2(x - 12) = 0 \\[1em] \Rightarrow (x + 2)(x - 12) = 0 \\[1em] \Rightarrow x = -2 \text{ or } x = 12.$

Hence, value of x = -2 or 12.