Using factorization, solve x^2 + 10x + 24 = 0

To factorize the equation we need to find two numbers a and b such that
a * b = 24 and
a + b = 10
By closely looking at those, we find that 4 and 6 satisfy both conditions, as
6 + 4 = 10 and
6 * 4 = 24
The next step is to split the middle term 10x into 6x + 4x, getting
x^2 + 6x + 4x + 24 = 0
Now we group the first two and the last two terms
x(x + 6) + 4(x + 6) = 0 Therefore,
(x+6)(x+4) = 0
For this to be true, at least one of the brackets needs to be 0.
For x + 6 = 0 we get x = -6
For x + 4 = 0 we get x = -4
Therefore, the set of solutions is S = {-6, -4}