SOLUTION: need help finding all solutions of this equation 9x^4+27x^3-4x^2-12x=0 please help...

Question 500997: need help finding all solutions of this equation 9x^4+27x^3-4x^2-12x=0 please help...
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
need help finding all solutions of this equation 9x^4+27x^3-4x^2-12x=0
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9x^4+27x^3-4x^2-12x=0
First factor out an x:
x(9x^3+27x^2-4x-12)=0
This gives one of the solutions, x = 0
Now we need to solve 9x^3+27x^2-4x-12=0
Factor by grouping:
(9x^3+27x^2) - (4x+12)
9x^2(x+3) - 4(x+3)
Since there is a common factor, x+3, by the distributive property we can write
(9x^2-4)(x+3)
The first expression is a difference of two squares:
9x^2-4 = (3x+2)(3x-2)
So the fully-factored equation is:
(3x+2)(3x-2)(x+3) = 0
So the other 3 solutions are:
x = -3, -2/3, 2/3
Graph is below:

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