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:

$$ a = 55 , b = -74 ~ \text{ and } ~ c = 24 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 55 }$ by the constant term $\color{blue}{c = 24} $.

$$ a \cdot c = 1320 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 1320 $ and add to $ b = -74 $.

Step 4: All pairs of numbers with a product of $ 1320 $ are:

PRODUCT = 1320
1     1320	-1     -1320
2     660	-2     -660
3     440	-3     -440
4     330	-4     -330
5     264	-5     -264
6     220	-6     -220
8     165	-8     -165
10     132	-10     -132
11     120	-11     -120
12     110	-12     -110
15     88	-15     -88
20     66	-20     -66
22     60	-22     -60
24     55	-24     -55
30     44	-30     -44
33     40	-33     -40

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -74 }$

PRODUCT = 1320 and SUM = -74
1     1320	-1     -1320
2     660	-2     -660
3     440	-3     -440
4     330	-4     -330
5     264	-5     -264
6     220	-6     -220
8     165	-8     -165
10     132	-10     -132
11     120	-11     -120
12     110	-12     -110
15     88	-15     -88
20     66	-20     -66
22     60	-22     -60
24     55	-24     -55
30     44	-30     -44
33     40	-33     -40

Step 6: Replace middle term $ -74 x $ with $ -30x-44x $:

$$ 55x^{2}-74x+24 = 55x^{2}-30x-44x+24 $$

Step 7: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 55x^{2}-30x-44x+24 = 5x\left(11x-6\right) -4\left(11x-6\right) = \left(5x-4\right) \left(11x-6\right) $$

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