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:

$$ a = 7 , b = -2 ~ \text{ and } ~ c = -5 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 7 }$ by the constant term $\color{blue}{c = -5} $.

$$ a \cdot c = -35 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -35 $ and add to $ b = -2 $.

Step 4: All pairs of numbers with a product of $ -35 $ are:

PRODUCT = -35
-1     35	1     -35
-5     7	5     -7

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -2 }$

PRODUCT = -35 and SUM = -2
-1     35	1     -35
-5     7	5     -7

Step 6: Replace middle term $ -2 x $ with $ 5x-7x $:

$$ 7x^{2}-2x-5 = 7x^{2}+5x-7x-5 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -1 $ out of the last two terms.

$$ 7x^{2}+5x-7x-5 = x\left(7x+5\right) -1\left(7x+5\right) = \left(x-1\right) \left(7x+5\right) $$

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