1. **State the problem:** Solve the equation $ (x-1)^2 = 2(x-1) $. 2. **Rewrite the equation:** The equation is $ (x-1)^2 = 2(x-1) $. 3. **Use the zero product property:** Move all terms to one side: $$ (x-1)^2 - 2(x-1) = 0 $$ 4. **Factor the expression:** Factor out the common term $ (x-1) $: $$ (x-1)\big((x-1) - 2\big) = 0 $$ 5. **Simplify inside the parentheses:** $$ (x-1)(x-1-2) = (x-1)(x-3) = 0 $$ 6. **Apply zero product rule:** Set each factor equal to zero: $$ x-1=0 \quad \text{or} \quad x-3=0 $$ 7. **Solve each equation:** $$ x=1 \quad \text{or} \quad x=3 $$ **Final answer:** The solutions are $ x=1 $ and $ x=3 $.