What is the set of solutions of |x^2+2x+3|<|x^2+2x-3|?

Answer 1

x^2+2x+3 = x^2 + 2x - 3 or x^2+2x+3 = -x^2 - 2x + 3

the first equation leads to a dead-end

3 = -3

2nd equation:

2x^2 + 4x = 0

2x(x+2) = 0

x=0 or x=-2

Both of these solutions work