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x^4 - 2x^3 - 15x^2 ≥  0       factor

x^2  ( x^2 - 2x - 15) ≥  0

x^2  ( x - 5) ( x + 3) ≥ 0

We have  four  intervals to consider

(-inf, -3] ,   [ -3, 0]  ,   [ 0 , 5 ]    and   [ 5, inf )

Picking a point in the first interval  and last interval    make the original inequality true

So....the solution  is

(-inf, -3 ] U  [ 5, inf )

Here's a graph  :

https://www.desmos.com/calculator/gzqfvkq87a

Solve x^4 - 2x^3 - 15x^2 >= 0.  Show all your steps!