Solve the following equation by factorisation:

x² - 3x - 10 = 0

Given,

$x^2 - 3x - 10 = 0 \\[0.5em] \Rightarrow x^2 - 5x + 2x - 10 = 0 \\[0.5em] \Rightarrow x(x - 5) + 2(x - 5) = 0 \\[0.5em] \Rightarrow (x + 2)(x - 5) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow x + 2 = 0 \text{ or } x - 5 = 0 \text{ ( Zero - product rule) }\\[0.5em] \Rightarrow x = -2 \text{ or } x = 5$

Hence, the roots of given equation are -2, 5.