I can not figure this question out Solve the equation by fac

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

15x^2 + 11x - 56 = 0

Is this even possible?

Solution

I will show you a trick that solves all this kind of problems.

15X2 + 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 X2 + 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.