college algebra

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Solve the following inequality.

x^3+9x^2-108 less or equal to 0.
Then write your solution in interval notation. I am sooo confused and do not have any idea how to do this. Can someone please show me step by step please???

Thanks in advance. Someone who is confused.

  • college algebra -

    This polynomial graphing might help sometimes:
    http://mathportal.org/calculators/polynomials-solvers/polynomial-graphing-calculator.php

    zeros at x = -6 (double zero) and x = +3
    so we really have
    (x+6)(x+6)(x-3)

    It is negative for large negative x
    it comes up and bounces off the x axis at x=-6, dropping down negative again
    it does not actually come up and cross the x axis until x = 3
    from then on it is positive,
    therefore negative for
    x</= +3 except for touching zero at x = -6

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