6) \( w^{2}-5 w=0 \)

To solve the equation \( w^2 - 5w = 0 \), you can factor out a 'w' from the equation. This gives you \( w(w - 5) = 0 \). Now, set each factor equal to zero: \( w = 0 \) or \( w - 5 = 0 \), leading to \( w = 5 \). So, the solutions are \( w = 0 \) and \( w = 5 \). This is a prime example of using factoring to solve quadratic equations! It’s a fun way to see how numbers can interact with one another and find hidden relationships within an equation. Plus, it highlights the importance of knowing your factor pairs!