How do you solve the quadratic equation x^2+7x+12=0

To solve quadratic equations we first need to factorise the equation into brackets. We can do this by looking at the numbers in the quadratic equation. The only number that isn't an x coefficient is the 12, this means that our 2 numbers in the bracket must multiply together to make positive 12. Both numbers will have to be positive or they will both have to be negative to make sure when they're multiplied together they make positive 12. These 2 numbers also have to add up to the number in front of the x, so in this case positive 7. If we take positive 3 and positive 4, they multiply to make 12 and add up to 7. This means they are the numbers we can put in our brackets so we would have (x+3)(x+4)=0 if you multiply this out you will get back to x²+7x+12=0. To find x we look at both brackets individually, if we set x+3=0 then that gives us x=-3. If we set x+4=0 then that gives us x=--4. This means our 2 roots are -3,-4.