Question

I am not sure how we get 0=-1(x-2)(x+4) because we also can get 0=-1(x+2)(x-4). How do we determine which to put?

Answer 1

0 = -1(x-2)(x+4) is not equivalent to 0 = -1(x+2)(x-4)

You have:

0 = -1(x-2)(x+4)

which means that

0 = (x-2)(x+4)

Multiplying by -1 at both sides:

(-1)*0 = (-1)*(x-2)(x+4)

0 = (-x + 2)(x + 4)

Multiplying by -1 at both sides again:

(-1)*0 = (-x + 2)(x + 4)*(-1)

0 = (-x + 2)(-x - 4)

Multiplying by -1 at both sides again:

(-1)*0 = (-1)*(-x + 2)(-x - 4)

0 = -1(-x + 2)(-x - 4)

which is different from

0 = -1(x+2)(x-4)