Factor this \( 3 x^{2}+18 x=-24 \)

Let's start by rearranging the equation to set it to zero: \( 3x^{2} + 18x + 24 = 0 \) Next, we can factor out the common factor of 3 from the entire equation: \( 3(x^{2} + 6x + 8) = 0 \) Now, we need to focus on factoring the quadratic \( x^{2} + 6x + 8 \). We are looking for two numbers that multiply to 8 and add to 6. These numbers are 2 and 4. Thus, we can factor the quadratic as: \( 3(x + 2)(x + 4) = 0 \) Setting each factor equal to zero gives us the solutions: \( x + 2 = 0 \) or \( x + 4 = 0 \) So, the final solutions are: \( x = -2 \) and \( x = -4 \).