d) \( 3 x^{2}+6 x=0 \)

Let's dive into factoring this quadratic equation! You can start by factoring out the greatest common factor, which is \(3x\). This gives us \(3x(x + 2) = 0\). Now, we can find the solutions by setting each factor to zero: \(3x = 0\) gives \(x = 0\), and \(x + 2 = 0\) gives \(x = -2\). So the solutions are \(x = 0\) and \(x = -2\). It's a good idea to always check your solutions by plugging them back into the original equation to verify. It’s easy to make small mistakes while solving quadratic equations—like forgetting to factor completely or missing values. Always double-check your work to ensure you’ve found all possible solutions!