Step 1 :

After factoring out $ 3 $ we have:

$$ 9x^{2}+42x+33 = 3 ( 3x^{2}+14x+11 ) $$

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:

$$ a = 3 , b = 14 ~ \text{ and } ~ c = 11 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 11} $.

$$ a \cdot c = 33 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 33 $ and add to $ b = 14 $.

Step 5: All pairs of numbers with a product of $ 33 $ are:

PRODUCT = 33
1     33	-1     -33
3     11	-3     -11

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 14 }$

PRODUCT = 33 and SUM = 14
1     33	-1     -33
3     11	-3     -11

Step 7: Replace middle term $ 14 x $ with $ 11x+3x $:

$$ 3x^{2}+14x+11 = 3x^{2}+11x+3x+11 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ 1 $ out of the last two terms.

$$ 3x^{2}+11x+3x+11 = x\left(3x+11\right) + 1\left(3x+11\right) = \left(x+1\right) \left(3x+11\right) $$

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