To solve this inequality, we need to first set it equal to 0:

-2x^2 < 4x

-2x^2 - 4x < 0

Now factor out -2x from both terms on the left side:

-2x(x + 2) < 0

Now we can find the critical points by setting each factor equal to 0:

-2x = 0
x = 0

x + 2 = 0
x = -2

Now we have the critical points at x = 0 and x = -2. We can create a number line and test the inequality for each interval:

Test x = -3:
-2(-3)(-3+2) < 0
6 > 0 (True)

Test x = -1:
-2(-1)(-1+2) < 0
2 < 0 (False)

Test x = 1:
-2(1)(1+2) < 0
-6 < 0 (True)

So the solution to the inequality is:
x is in the interval (-2, 0) U (0, infinity)