Step 1 :

After factoring out $ 10 $ we have:

$$ 20n^{2}-80n-70 = 10 ( 2n^{2}-8n-7 ) $$

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:

$$ a = 2 , b = -8 ~ \text{ and } ~ c = -7 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -7} $.

$$ a \cdot c = -14 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -14 $ and add to $ b = -8 $.

Step 5: All pairs of numbers with a product of $ -14 $ are:

PRODUCT = -14
-1     14	1     -14
-2     7	2     -7

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -8 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -8 }$, we conclude the polynomial cannot be factored.

Polynomial Factoring Calculator