To solve this inequality, we can first rewrite it in standard form:

-x^2 < 4x

Next, let's subtract 4x from both sides to get:

-x^2 - 4x < 0

Now, we can factor out a negative sign from the left side:

-x(x + 4) < 0

The inequality holds true when either:

From the first condition, we have:
-x < 0
x > 0

x + 4 > 0
x > -4

So, the solution for the first condition is:
0 < x < 4

From the second condition, we have:
-x > 0
x < 0

x + 4 < 0
x < -4

So, the solution for the second condition is:
x < -4

Putting it all together, the solution to the original inequality is:
-4 < x < 0