Zeroes:
We must solve

To do so, we define the auxiliary variable
. The equation becomes

The quadratic formula yields the solutions

Substituting back
gives

So, the zeroes are -6, -3, 3, 6.
Turning points:
Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.
We have

If we set the derivative to be zero, we have

So, the derivative is zero if x=0 or
