Step 1: 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:

$$ a = 40 , b = 19 ~ \text{ and } ~ c = -14 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 40 }$ by the constant term $\color{blue}{c = -14} $.

$$ a \cdot c = -560 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -560 $ and add to $ b = 19 $.

Step 4: All pairs of numbers with a product of $ -560 $ are:

PRODUCT = -560
-1     560	1     -560
-2     280	2     -280
-4     140	4     -140
-5     112	5     -112
-7     80	7     -80
-8     70	8     -70
-10     56	10     -56
-14     40	14     -40
-16     35	16     -35
-20     28	20     -28

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 19 }$

PRODUCT = -560 and SUM = 19
-1     560	1     -560
-2     280	2     -280
-4     140	4     -140
-5     112	5     -112
-7     80	7     -80
-8     70	8     -70
-10     56	10     -56
-14     40	14     -40
-16     35	16     -35
-20     28	20     -28

Step 6: Replace middle term $ 19 x $ with $ 35x-16x $:

$$ 40x^{2}+19x-14 = 40x^{2}+35x-16x-14 $$

Step 7: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -2 $ out of the last two terms.

$$ 40x^{2}+35x-16x-14 = 5x\left(8x+7\right) -2\left(8x+7\right) = \left(5x-2\right) \left(8x+7\right) $$

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