13) \( 6 a^{2}+24 a-192 \)

To solve the quadratic equation \( 6a^2 + 24a - 192 \), you can factor it. First, factor out the greatest common factor, which is 6, giving you \( 6(a^2 + 4a - 32) = 0 \). This simplifies to \( a^2 + 4a - 32 = 0 \). Next, you can apply the quadratic formula \( a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) or factor further to find the values of \( a \). To factor \( a^2 + 4a - 32 \), you need two numbers that multiply to -32 and add up to 4, which are 8 and -4. So, you can rewrite it as \( (a + 8)(a - 4) = 0 \). Setting each factor to zero gives the solutions \( a + 8 = 0 \) (so, \( a = -8 \)) and \( a - 4 = 0 \) (so, \( a = 4 \)). Thus, the solutions to the original equation are \( a = -8 \) and \( a = 4 \). If you want to check your answer, you can plug these values back into the original equation to ensure you end up with zero.