\(x\left(1-2y\right)+y-\frac{1}{2}=-\frac{1}{2}\)
\(x\left(1-2y\right)+\frac{1}{2}\left(2y-1\right)=-\frac{1}{2}\)
\(\left(x-\frac{1}{2}\right)\left(1-2y\right)=-\frac{1}{2}\)
\(x\left(1-2y\right)+y-\frac{1}{2}=-\frac{1}{2}\)
\(x\left(1-2y\right)+\frac{1}{2}\left(2y-1\right)=-\frac{1}{2}\)
\(\left(x-\frac{1}{2}\right)\left(1-2y\right)=-\frac{1}{2}\)