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:

$$ a = 9 , b = -30 ~ \text{ and } ~ c = 16 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 16} $.

$$ a \cdot c = 144 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 144 $ and add to $ b = -30 $.

Step 4: All pairs of numbers with a product of $ 144 $ are:

PRODUCT = 144
1     144	-1     -144
2     72	-2     -72
3     48	-3     -48
4     36	-4     -36
6     24	-6     -24
8     18	-8     -18
9     16	-9     -16
12     12	-12     -12

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -30 }$

PRODUCT = 144 and SUM = -30
1     144	-1     -144
2     72	-2     -72
3     48	-3     -48
4     36	-4     -36
6     24	-6     -24
8     18	-8     -18
9     16	-9     -16
12     12	-12     -12

Step 6: Replace middle term $ -30 x $ with $ -6x-24x $:

$$ 9x^{2}-30x+16 = 9x^{2}-6x-24x+16 $$

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

$$ 9x^{2}-6x-24x+16 = 3x\left(3x-2\right) -8\left(3x-2\right) = \left(3x-8\right) \left(3x-2\right) $$

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