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# Factoring?

I can not figure this question out..
Solve the equation by factoring:

15x^2 + 11x - 56 = 0

Is this even possible?

15x2 + 11x - 56 = 0

Let's break this down...
15x2
(x)(x)=x2
(5)(3)=15 or (15)(1)=15

11x
11x=(11x+0x) or (10x+1x) or (9x+2x), etc

-56
(-8)(7) or (8)(-7)

Let's factor...
15x2 + 11x - 56 = 0
(?x+  ??)(?x-  ??)

Because the 11x is positive, the added ??x must be greater than the subtracted ??x.
(3x+7)(5x-8)=0
Let's FOIL...
FIRST.....15x2
OUTER...-24x
INNER.....35x
LAST.......56

15x2-24x+35x+56=0
15x2+11x-56=0

Thank you!
You are SOOOOO welcome.
Keep those questions coming.
I will show you a trick that solves all this kind of problems.

15X+ 11X - 56

A quadratic like this can only be factorable, if  There exist 2 rational numbers whose Sum is 11, and
their product is  - 15 * 56

So we rite 15 * 56  as product of its factor

15 * 56 =  3 * 5 * 7 * 8 = 15 * 56 = 35 * 24 =

Now we see that  the difference of 35 and 24 is 11

15 X+ 35X - 24X -56   ( break up 11X into 35X- 24X)

5X( 3X +7 )  - 8 ( 3X + 7)  , Now 2 terms have common factor  of (3X +7 )

( 3X + 7 ) ( 5X - 8 )    This is the final answer.