How do I solve this problem? 12x^4+4x^3-108x^2-36x=0

I need step-by-step instructions so I can try and get it. There are suppose to be 4 solutions solving for x.

12x^4+4x^3-108x^2-36x=0

3x^4 + x^3 - 27x² - 9x = 0
x(3x³ + x² - 27x - 9) = 0
x[x²(3x + 1) - 9(3x + 1) = 0
x(x²-9)(3x+1) = 0
x(x+3)(x-3)(3x+1) = 0
From the zero product rule:
x = 0
x+3 = 0
x-3 = 0
3x+1 = 0
or:
x = -3, -1/3, 0, 3

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