Solve for x in \( x^{2}-6 x=0 \)

To solve the equation \( x^{2}-6x=0 \), you can factor out an \( x \) from the left-hand side, giving you \( x(x-6)=0 \). This product is equal to zero if either \( x=0 \) or \( x-6=0 \). Therefore, the solutions are \( x=0 \) and \( x=6 \). Now, let’s put these solutions to good use! You can plug them back into the original equation to verify; it’s a great way to ensure you didn't miss anything. If you check both solutions, they hold true, making your skills in solving quadratic equations shine bright!