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:

$$ a = 9 , b = -56 ~ \text{ and } ~ c = 12 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 12} $.

$$ a \cdot c = 108 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 108 $ and add to $ b = -56 $.

Step 4: All pairs of numbers with a product of $ 108 $ are:

PRODUCT = 108
1     108	-1     -108
2     54	-2     -54
3     36	-3     -36
4     27	-4     -27
6     18	-6     -18
9     12	-9     -12

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -56 }$

PRODUCT = 108 and SUM = -56
1     108	-1     -108
2     54	-2     -54
3     36	-3     -36
4     27	-4     -27
6     18	-6     -18
9     12	-9     -12

Step 6: Replace middle term $ -56 x $ with $ -2x-54x $:

$$ 9x^{2}-56x+12 = 9x^{2}-2x-54x+12 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -6 $ out of the last two terms.

$$ 9x^{2}-2x-54x+12 = x\left(9x-2\right) -6\left(9x-2\right) = \left(x-6\right) \left(9x-2\right) $$

Polynomial Factoring Calculator