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:

$$ a = 7 , b = -48 ~ \text{ and } ~ c = -7 $$

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

$$ a \cdot c = -49 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -49 $ and add to $ b = -48 $.

Step 4: All pairs of numbers with a product of $ -49 $ are:

PRODUCT = -49
-1     49	1     -49
-7     7	7     -7

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -48 }$

PRODUCT = -49 and SUM = -48
-1     49	1     -49
-7     7	7     -7

Step 6: Replace middle term $ -48 x $ with $ x-49x $:

$$ 7x^{2}-48x-7 = 7x^{2}+x-49x-7 $$

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

$$ 7x^{2}+x-49x-7 = x\left(7x+1\right) -7\left(7x+1\right) = \left(x-7\right) \left(7x+1\right) $$

Polynomial Factoring Calculator