e) \( 2 x^{2}-2 x=4 \)

Solve the equation \( 2x^{2}-2x=4 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(2x^{2}-2x=4\) - step1: Move the expression to the left side: \(2x^{2}-2x-4=0\) - step2: Factor the expression: \(2\left(x-2\right)\left(x+1\right)=0\) - step3: Divide the terms: \(\left(x-2\right)\left(x+1\right)=0\) - step4: Separate into possible cases: \(\begin{align}&x-2=0\\&x+1=0\end{align}\) - step5: Solve the equation: \(\begin{align}&x=2\\&x=-1\end{align}\) - step6: Rewrite: \(x_{1}=-1,x_{2}=2\) The solutions to the equation \(2x^{2}-2x=4\) are \(x=-1\) and \(x=2\).