-2*x*(x+1)*(x-1)>0
1) Let's solve in ℝ: -2x·(x + 1)·(x -1) > 0
We study the sign of each factor of the product
⇥The expression -2x is zero at:
⇥ x = 0
⇥Its coefficient of x, -2, being negative, it is positive before and negative after 0
⇥The expression x + 1 is zero at x = -1, it is negative before and positive after
⇥The expression x -1 is zero at x = 1, it is negative before and positive after
2) Let's draw up the sign table:
x-∞ -1 0 1 +∞
-2x++0--
x + 1-0+++
x -1---0+
-2x·(x + 1)·(x -1)+0-0+0-
▶Solution obtained: x ∈ (-∞, -1) ∪ (0, 1)