Auivaules: \( \left(E_{1}\right)=(x-1)(2 x-3)=0 \)

Did you know that the solutions to this equation come from setting each factor to zero? So, you get \(x-1=0\) leading to \(x=1\) and \(2x-3=0\), which yields \(x=\frac{3}{2}\). These roots are \(x=1\) and \(x=1.5\), basically finding where our equation intersects the x-axis! When solving polynomial equations like this, a common mistake is to forget that both factors need to equal zero. Also, ensure you fully factor the polynomial, as overlooking a common factor can lead to missing roots. Always double-check your factored form!