Answer:
Step-by-step explanation:
6x² -5x -56 = 0 . . . . . subtract the constant
(3x +8)(2x -7) = 0 . . . .factor*
The zero product property says the product will be zero only when one (or both) of the factors is zero.
First Factor
... 3x +8 = 0
... x + 8/3 = 0 . . . . divide by the coefficient of x
... x = -8/3 . . . . . . subtract 8/3
Second Factor
... 2x -7 = 0 . . . . . . set the factor to zero
... x -7/2 = 0 . . . . . divide by the coefficient of x
... x = 7/2 . . . . . . . add 7/2
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*Comment on factoring
There are various ways to do this. In basic terms, we want to find numbers that are factors of the product 6·(-56) whose sum is -5. We found those numbers to be -21 and 16. Then we can rewrite the -5x term using these numbers and factor by grouping.
... 6x² -5x -56 = (6x² -21x) +(16x -56) = 3x(2x -7) +8(2x -7) = (3x +8)(2x -7)
