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:

$$ a = 9 , b = 24 ~ \text{ and } ~ c = 7 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = 7} $.

$$ a \cdot c = 63 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 63 $ and add to $ b = 24 $.

Step 4: All pairs of numbers with a product of $ 63 $ are:

PRODUCT = 63
1     63	-1     -63
3     21	-3     -21
7     9	-7     -9

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 24 }$

PRODUCT = 63 and SUM = 24
1     63	-1     -63
3     21	-3     -21
7     9	-7     -9

Step 6: Replace middle term $ 24 x $ with $ 21x+3x $:

$$ 9x^{2}+24x+7 = 9x^{2}+21x+3x+7 $$

Step 7: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ 1 $ out of the last two terms.

$$ 9x^{2}+21x+3x+7 = 3x\left(3x+7\right) + 1\left(3x+7\right) = \left(3x+1\right) \left(3x+7\right) $$

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