Step 1 :

After factoring out $ -1 $ we have:

$$ -9x^{2}-22x-8 = - ~ ( 9x^{2}+22x+8 ) $$

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:

$$ a = 9 , b = 22 ~ \text{ and } ~ c = 8 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 8} $.

$$ a \cdot c = 72 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 72 $ and add to $ b = 22 $.

Step 5: All pairs of numbers with a product of $ 72 $ are:

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

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 22 }$

PRODUCT = 72 and SUM = 22
1     72	-1     -72
2     36	-2     -36
3     24	-3     -24
4     18	-4     -18
6     12	-6     -12
8     9	-8     -9

Step 7: Replace middle term $ 22 x $ with $ 18x+4x $:

$$ 9x^{2}+22x+8 = 9x^{2}+18x+4x+8 $$

Step 8: Apply factoring by grouping. Factor $ 9x $ out of the first two terms and $ 4 $ out of the last two terms.

$$ 9x^{2}+18x+4x+8 = 9x\left(x+2\right) + 4\left(x+2\right) = \left(9x+4\right) \left(x+2\right) $$

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