a) \( (2 x-1)(4-4 x)=0 \)

To solve the equation \( (2x - 1)(4 - 4x) = 0 \), we can set each factor to zero. First, for \( 2x - 1 = 0 \), adding 1 to both sides gives us \( 2x = 1 \), which leads to \( x = \frac{1}{2} \). Now for the second factor \( 4 - 4x = 0 \), adding \( 4x \) to both sides yields \( 4 = 4x \), resulting in \( x = 1 \). Thus, the solutions are \( x = \frac{1}{2} \) and \( x = 1 \). Remember, whenever you have a product of factors equal to zero, at least one of the factors must also equal zero! This principle—also known as the Zero Product Property—can be a game-changer in solving quadratic equations and polynomials. To avoid minor mistakes, double-check that you simplify and solve each factor completely.