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Bot GPT 4-o mini Let's analyze Hyung-eun's steps:
1. The original equation is \( x^2 - 4x - 12 = 0 \).
2. **Step 1**: She rewrites the equation as \( x^2 + (-6x) + 2x - 12 = 0 \). The correct factoring should give two terms that combine to give \( -4x \) when summed. Here, she splits \( -4x \) into \( (-6x) + (2x) \), which is valid.
3. **Step 2**: She groups the terms as \( (x^2 + (-6x)) + (2x - 12) = 0 \). This step is still correct as she is grouping the terms.
4. **Step 3**: She factored it as \( x(x + (-6)) + 2(x - 6) = 0 \). However, the term \( 2(x - 6) \) is incorrect. The correct split from the previous grouping should yield \( 2(x + 6) \).
At this point, the error occurs in **Step 3**. The step should have involved factoring \( 2(x + 6) \) instead of \( 2(x - 6) \).
Thus, the first error occurs at **Step 3**.