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:

$$ a = 7 , b = -67 ~ \text{ and } ~ c = 36 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 7 }$ by the constant term $\color{blue}{c = 36} $.

$$ a \cdot c = 252 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 252 $ and add to $ b = -67 $.

Step 4: All pairs of numbers with a product of $ 252 $ are:

PRODUCT = 252
1     252	-1     -252
2     126	-2     -126
3     84	-3     -84
4     63	-4     -63
6     42	-6     -42
7     36	-7     -36
9     28	-9     -28
12     21	-12     -21
14     18	-14     -18

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -67 }$

PRODUCT = 252 and SUM = -67
1     252	-1     -252
2     126	-2     -126
3     84	-3     -84
4     63	-4     -63
6     42	-6     -42
7     36	-7     -36
9     28	-9     -28
12     21	-12     -21
14     18	-14     -18

Step 6: Replace middle term $ -67 x $ with $ -4x-63x $:

$$ 7x^{2}-67x+36 = 7x^{2}-4x-63x+36 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -9 $ out of the last two terms.

$$ 7x^{2}-4x-63x+36 = x\left(7x-4\right) -9\left(7x-4\right) = \left(x-9\right) \left(7x-4\right) $$

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