The factorization 2x(-7-6x) is not wrong because distributing the outer 2x to each term inside gets us
- 2x times -7 = -14x
- 2x times -6x = -12x^2
which leads back to -14x-12x^2
Therefore, 2x(-7-6x) = -14x - 12x^2 is true.
Convention usually has us pull out the negative so the terms inside are all positive. This is just a practice done. There technically isn't any right way vs wrong way to factor, when we compare the two different factorizations. I think it's more of a subjective style than anything.