Solve the quadratic equation x^2+5x+6=0

Quadratic equations are a slightly bit more tricky than other algebraic equations we might have seen before. They are called quadratic equations because one of the unknown values is squared (mutiplied by itself, e.g. 4^2=16). Importantly for us, this means there can be up to two possible roots of the equation. There are three main algebraic methods for solving a quadratic equation like this one; the method we will use is factorisation.
We want to simplify the expression x^2+5x+6 by factorising into two brackets.One bracket with have (x +- something) and the other (x+-something). These two somethings will multiply to make 6 and add to make 5. There is a little bit of trial and error involved in working about what these "somethings" are but if we have a basic understanding of factors, it is quite straightforward. The factors of 6 (in pairs) are 1, 6 2, 31 and 6 multiply to make 6 and add to make 7. 7 is not the coefficient of 5x so it is not this pair2 and 3 multiply to make 6 and add to make 5, which is the coefficient of 5x.Therefore, (x+2)(x+3)=0In order to satisfy this equation we need to find the values of x that make the result zero. To make the equation equal zero one (or both) of the brackets needs to equal zero. If x+2=0, x=-2 If x+3=0, x=-3Therefore x = -2 or -3