How do you factorise a simple quadratic equation?

Simple quadratic equations e.g. x²+5x + 6 = 0, can be solved by evaluating the second and third terms. Quadratic equations can be represented within two sets of brackets (x + a)(x + b). Using this template, we can identify that the second term +5(x) is equivalent to a+b and that the third term +6 is equivalent to ab. With trial and error, or simple substitution, we can solve these as simultaneous equations: a+b = 5 ab = 6to assess that x²+5x + 6 = 0 can be factorised into (x+3)(x+2).