SOLUTION: Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now th

Question 969380: Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now the equation looks like this:
15x^2 + 6x - 30x - 12. So I divide: 15x^2 + 6x/2x and -30x-12/-6 which now gave me 3x(5x+2)-6(5x+2) I continue to think my answer is (5x+2)(3x-6). unfortunately, the answer key has the answer as 3(5x+2)(x-2) what did I do wrong? Please help me.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Each term has a factor of 3:

There are only so few ways to factorize . Try a few combination of trinomial factorizations for the quadratic factor from the last step.

Look at the possible result for terms of x:

(5 2)(1 2)----------10 and 2, maybe.

(5 4)(1 1)---------5 and 4, NO.

(5 4 )(1 1)----------5 and 4, NO.

Look further at this: ;
You need and . Decide which signs within the binomials are needed.
......
This is what works: .

Your originally given expression also contained a factor of 3, so to finish your factorization of that, you have
.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now the equation looks like this:
15x^2 + 6x - 30x - 12. So I divide: 15x^2 + 6x/2x and -30x-12/-6 which now gave me 3x(5x+2)-6(5x+2) I continue to think my answer is (5x+2)(3x-6). unfortunately, the answer key has the answer as 3(5x+2)(x-2) what did I do wrong? Please help me.

First, this is NOT an equation, but a TRINOMIAL that can be FACTORED.

The first step you need to take is to find the GCF
------ Factoring out GCF, 3
----- Factoring trinomial in the parentheses
Your answer is PARTIALLY correct. Since you didn't factor out a GCF, you can see that one of your
binomials, (3x - 6) can be factored as: 3(x - 2), thereby giving you: 3(x - 2)(5x + 2), which is
the same as mine and the answer in the answer key.
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