To factor the quadratic equation \(x^2 + 14x + 24 = 0\), we need to find two numbers that multiply to 24 (the constant term) and add to 14 (the coefficient of the \(x\) term).
The numbers that satisfy these conditions are 12 and 2, because:
- \(12 \times 2 = 24\)
- \(12 + 2 = 14\)
Thus, we can factor the quadratic as follows:
\[ (x + 12)(x + 2) = 0 \]
So, the factored form of the equation \(x^2 + 14x + 24 = 0\) is:
\[ (x + 12)(x + 2) = 0 \]