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:

$$ a = 3 , b = -29 ~ \text{ and } ~ c = 56 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 56} $.

$$ a \cdot c = 168 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 168 $ and add to $ b = -29 $.

Step 4: All pairs of numbers with a product of $ 168 $ are:

PRODUCT = 168
1     168	-1     -168
2     84	-2     -84
3     56	-3     -56
4     42	-4     -42
6     28	-6     -28
7     24	-7     -24
8     21	-8     -21
12     14	-12     -14

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -29 }$

PRODUCT = 168 and SUM = -29
1     168	-1     -168
2     84	-2     -84
3     56	-3     -56
4     42	-4     -42
6     28	-6     -28
7     24	-7     -24
8     21	-8     -21
12     14	-12     -14

Step 6: Replace middle term $ -29 x $ with $ -8x-21x $:

$$ 3x^{2}-29x+56 = 3x^{2}-8x-21x+56 $$

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

$$ 3x^{2}-8x-21x+56 = x\left(3x-8\right) -7\left(3x-8\right) = \left(x-7\right) \left(3x-8\right) $$

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