$$ \begin{aligned} 2x+2\cdot(1-x) &= 0&& \text{simplify left side} \\[1 em]2x+2-2x &= 0&& \\[1 em]2 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 2 = 0 } $ is FALSE, we conclude that the equation has no solution.
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