Step 1 :

After factoring out $ 7 $ we have:

$$ 63x^{2}-168x+49 = 7 ( 9x^{2}-24x+7 ) $$

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:

$$ a = 9 , b = -24 ~ \text{ and } ~ c = 7 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 7} $.

$$ a \cdot c = 63 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 63 $ and add to $ b = -24 $.

Step 5: All pairs of numbers with a product of $ 63 $ are:

PRODUCT = 63
1     63	-1     -63
3     21	-3     -21
7     9	-7     -9

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -24 }$

PRODUCT = 63 and SUM = -24
1     63	-1     -63
3     21	-3     -21
7     9	-7     -9

Step 7: Replace middle term $ -24 x $ with $ -3x-21x $:

$$ 9x^{2}-24x+7 = 9x^{2}-3x-21x+7 $$

Step 8: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ -7 $ out of the last two terms.

$$ 9x^{2}-3x-21x+7 = 3x\left(3x-1\right) -7\left(3x-1\right) = \left(3x-7\right) \left(3x-1\right) $$

Polynomial Factoring Calculator