Step 1 :

After factoring out $ -5 $ we have:

$$ -25x^{2}+215x-280 = -5 ( 5x^{2}-43x+56 ) $$

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:

$$ a = 5 , b = -43 ~ \text{ and } ~ c = 56 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = 56} $.

$$ a \cdot c = 280 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 280 $ and add to $ b = -43 $.

Step 5: All pairs of numbers with a product of $ 280 $ are:

PRODUCT = 280
1     280	-1     -280
2     140	-2     -140
4     70	-4     -70
5     56	-5     -56
7     40	-7     -40
8     35	-8     -35
10     28	-10     -28
14     20	-14     -20

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -43 }$

PRODUCT = 280 and SUM = -43
1     280	-1     -280
2     140	-2     -140
4     70	-4     -70
5     56	-5     -56
7     40	-7     -40
8     35	-8     -35
10     28	-10     -28
14     20	-14     -20

Step 7: Replace middle term $ -43 x $ with $ -8x-35x $:

$$ 5x^{2}-43x+56 = 5x^{2}-8x-35x+56 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -7 $ out of the last two terms.

$$ 5x^{2}-8x-35x+56 = x\left(5x-8\right) -7\left(5x-8\right) = \left(x-7\right) \left(5x-8\right) $$

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