Solve for \( x \) : \( x(x-2)=0 \)

To solve the equation \( x(x-2)=0 \), you can use the zero product property, which states that if the product of two factors equals zero, at least one of the factors must also equal zero. Here, our factors are \( x \) and \( (x-2) \). Setting each factor to zero gives: 1. \( x = 0 \) 2. \( x - 2 = 0 \) → \( x = 2 \) Thus, the solutions for \( x \) are \( x = 0 \) and \( x = 2 \).