Solve the following equation by factorisation:

a²x² + (a² + b²)x + b² = 0, a ≠ 0.

Given,

$a^2x^2 + (a^2 + b^2)x + b^2 = 0 \\[0.5em] \Rightarrow a^2x^2 + a^2x + b^2x + b^2 = 0 \\[0.5em] \Rightarrow a^2x(x + 1) + b^2(x + 1) = 0 \\[0.5em] \Rightarrow (a^2x + b^2)(x + 1) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow a^2x + b^2 = 0 \text{ or } x + 1 = 0 \text{ (Zero-product rule) } \\[0.5em] \Rightarrow a^2x = -b^2 \text{ or } x = -1 \\[0.5em] \Rightarrow x = -\dfrac{b^2}{a^2} \text{ or } x =-1 \\[0.5em]$

Hence, the roots of given equation are $-\dfrac{b^2}{a^2}, -1.$