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:

$$ a = 33 , b = 20 ~ \text{ and } ~ c = 3 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 33 }$ by the constant term $\color{blue}{c = 3} $.

$$ a \cdot c = 99 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 99 $ and add to $ b = 20 $.

Step 4: All pairs of numbers with a product of $ 99 $ are:

PRODUCT = 99
1     99	-1     -99
3     33	-3     -33
9     11	-9     -11

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 20 }$

PRODUCT = 99 and SUM = 20
1     99	-1     -99
3     33	-3     -33
9     11	-9     -11

Step 6: Replace middle term $ 20 x $ with $ 11x+9x $:

$$ 33x^{2}+20x+3 = 33x^{2}+11x+9x+3 $$

Step 7: Apply factoring by grouping. Factor $ 11x $ out of the first two terms and $ 3 $ out of the last two terms.

$$ 33x^{2}+11x+9x+3 = 11x\left(3x+1\right) + 3\left(3x+1\right) = \left(11x+3\right) \left(3x+1\right) $$

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