d. \( 5 x^{2}-5 x=0 \)

To solve the equation \( 5x^2 - 5x = 0 \), you can factor out the common term, which is \( 5x \). This gives you \( 5x(x - 1) = 0 \). Now, you can set each factor equal to zero: \( 5x = 0 \) or \( x - 1 = 0 \). From \( 5x = 0 \), you find \( x = 0 \), and from \( x - 1 = 0 \), you find \( x = 1 \). Thus, the solutions are \( x = 0 \) and \( x = 1 \). Additionally, both solutions illustrate interesting points: \( x = 0 \) gives us the origin of the parabola represented by the quadratic equation, and \( x = 1 \) is where it touches the x-axis again. This visual insight can help cement your understanding of quadratic roots!