Solve each of the following equations. (a) \( (2 x-1)(x+8)=0 \)

To solve the equation \( (2x-1)(x+8)=0 \), we use the zero product property, which states that if the product of two factors is zero, at least one of the factors must be zero. First, set each factor to zero: 1. \( 2x-1=0 \) Solving for \( x \), we add 1 to both sides to get \( 2x=1 \), then divide by 2, yielding \( x=\frac{1}{2} \). 2. \( x+8=0 \) Solving for \( x \), we subtract 8 from both sides, resulting in \( x=-8 \). Thus, the solutions to the equation are \( x=\frac{1}{2} \) and \( x=-8 \).