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:

$$ a = 9 , b = -101 ~ \text{ and } ~ c = 232 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 232} $.

$$ a \cdot c = 2088 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 2088 $ and add to $ b = -101 $.

Step 4: All pairs of numbers with a product of $ 2088 $ are:

PRODUCT = 2088
1     2088	-1     -2088
2     1044	-2     -1044
3     696	-3     -696
4     522	-4     -522
6     348	-6     -348
8     261	-8     -261
9     232	-9     -232
12     174	-12     -174
18     116	-18     -116
24     87	-24     -87
29     72	-29     -72
36     58	-36     -58

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -101 }$

PRODUCT = 2088 and SUM = -101
1     2088	-1     -2088
2     1044	-2     -1044
3     696	-3     -696
4     522	-4     -522
6     348	-6     -348
8     261	-8     -261
9     232	-9     -232
12     174	-12     -174
18     116	-18     -116
24     87	-24     -87
29     72	-29     -72
36     58	-36     -58

Step 6: Replace middle term $ -101 x $ with $ -29x-72x $:

$$ 9x^{2}-101x+232 = 9x^{2}-29x-72x+232 $$

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

$$ 9x^{2}-29x-72x+232 = x\left(9x-29\right) -8\left(9x-29\right) = \left(x-8\right) \left(9x-29\right) $$

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