Step 1 :

After factoring out $ -1 $ we have:

$$ -2x^{2}+9x+56 = - ~ ( 2x^{2}-9x-56 ) $$

Step 2 :

Step 2: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 2 , b = -9 ~ \text{ and } ~ c = -56 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -56} $.

$$ a \cdot c = -112 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -112 $ and add to $ b = -9 $.

Step 5: All pairs of numbers with a product of $ -112 $ are:

PRODUCT = -112
-1     112	1     -112
-2     56	2     -56
-4     28	4     -28
-7     16	7     -16
-8     14	8     -14

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -9 }$

PRODUCT = -112 and SUM = -9
-1     112	1     -112
-2     56	2     -56
-4     28	4     -28
-7     16	7     -16
-8     14	8     -14

Step 7: Replace middle term $ -9 x $ with $ 7x-16x $:

$$ 2x^{2}-9x-56 = 2x^{2}+7x-16x-56 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -8 $ out of the last two terms.

$$ 2x^{2}+7x-16x-56 = x\left(2x+7\right) -8\left(2x+7\right) = \left(x-8\right) \left(2x+7\right) $$

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