Solve the following equation by factorisation:

x² - 4x - 12 = 0 when x ∈ N

Given,

$x^2 - 4x - 12 = 0 \\[0.5em] \Rightarrow x^2 - 6x + 2x - 12 = 0 \\[0.5em] \Rightarrow x(x - 6) + 2(x - 6) = 0 \\[0.5em] \Rightarrow (x + 2)(x - 6) = 0 \text{ (Factorising left side) }\\[0.5em] \Rightarrow x + 2 = 0 \text{ or } x - 6 = 0 \text{ (Zero-product rule) } \\[0.5em] \Rightarrow x = -2 \text{ or } x = 6$

Since x ∈ N hence x = -2 is not the root.
Hence, the root of given equation is 6.