The final factored form of this is 3x(x + 8) = 0
In order to find this, we need to find the greatest common denominator of the coefficients. To do that, we can list the factors of each number.
Factors of 3: 1, 3
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The greatest factor that they share is 3. Therefore we can factor out a 3.
3(x^2 + 8x) = 0
Now we look for how many x's we can take out. Since each have at least one x, we take out 1 x.
3x(x + 8) = 0