SOLUTION: solve the equation 8x^3 + 4x^2 - 18x - 9 = 0 algebraically for all values of x?

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Question 243649: solve the equation 8x^3 + 4x^2 - 18x - 9 = 0 algebraically for all values of x?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

8x%5E3+%2B+4x%5E2+-+18x+-+9+=+0

Factor 4x%5E2 out of the first two terms:

4x%5E2%282x+%2B+1%29+-+18x+-+9+=+0

Factor -9 out of the last two terms on the left:

4x%5E2%282x+%2B+1%29+-9%282x+%2B+1%29+=+0

Factor %282x%2B1%29 out of both terms on the left:

%282x%2B1%29%284x%5E2-9%29=0

Factor the expression in the second parentheses as 
the difference of squares:

%282x%2B1%29%282x-3%29%282x%2B3%29=0

Use the zero factor principle:
Set each of the three factors = 0:

2x%2B1=0
2x=-1
x=-1%2F2

2x-3=0
2x=3
x=3%2F2

2x%2B3=0
2x=-3
x=-3%2F2

Those are the three solutions.

Edwin