SOLUTION: Tutor: How do I factor by grouping: 18a^3-24a^2b+15ab^2-20b^3 and How do I solve the following 18x^2+9x-2=0 I'm just not getting this one, I keep coming up with X=0...I'm lost

Algebra ->  Equations -> SOLUTION: Tutor: How do I factor by grouping: 18a^3-24a^2b+15ab^2-20b^3 and How do I solve the following 18x^2+9x-2=0 I'm just not getting this one, I keep coming up with X=0...I'm lost      Log On


   

Question 86473: Tutor: How do I factor by grouping: 18a^3-24a^2b+15ab^2-20b^3 and
How do I solve the following 18x^2+9x-2=0 I'm just not getting this one, I keep coming up with X=0...I'm lost!
Thank you
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
The first question is factor on grouping:

18a%5E3+-+24a%5E2b+%2B+15ab%5E2+-+20b%5E3

Between the first two terms we find 6a%5E2 as the common factor and the next two terms we find 5b%5E2 as a common factor.

Hence, the above equation can be written as:

%286a%5E2+%283a+-+4b%29%29+%2B+%285b%5E2%283a+-+4b%29%29

Here we observe that (3a - 4b) is a common factor between the terms.

+%283a+-+4b%29%286a%5E2+%2B+5b%5E2%29

Thus, the solution.

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The second Probelm is to factorize the given quadratic equation.

The given expression is:

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

==> The middle terms can be factored as +12x and a -3x which when multiplied gives us -36x%5E2

Hence, this can be written as:

18x%5E2+%2B+12x+-+3x+-+2+=+0+

6x%283x+%2B+2%29-+1%283x+%2B+2%29+=+0+

==> (3x + 2)(6x - 1) = 0

==> Which implies that either of them is equal to zero.

(3x + 2) = 0 OR (6x - 1) = 0

==> 3x = - 2 OR 6x = 1

==> x+=+%28-2%2F3%29 OR x = %281%2F6%29

Hence, the solution.

Regards