Use factorisation to solve the equation x^2+5x+6=0

As we are considering a quadratic equation, we are looking for two values of x that make the equation equal to 0. To factorise, first look to the constant term (the term without any x) to find 2 numbers that multiply to make +6. These are +1 and +6, -1 and -6, +2 and +3, and -2 and -3. Now we look to the x term in the equation, here +5x, to find which of these pairs add together to make +5. This is +2 and +3. Hence the factorisation of the equation is given by (x +2)(x +3) = 0 , and this can be checked by multiplying out the brackets to reach the original equation (for example, using the FOIL method.) Solving the equation now follows from finding the two values of x that make each of the two brackets equal to 0. This is the same as solving the equations x+2=0 and x+3=0. Hence the two solutions to this equation are x=-2 and x=-3.