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:

$$ a = 10 , b = 43 ~ \text{ and } ~ c = 28 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 10 }$ by the constant term $\color{blue}{c = 28} $.

$$ a \cdot c = 280 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 280 $ and add to $ b = 43 $.

Step 4: All pairs of numbers with a product of $ 280 $ are:

PRODUCT = 280
1     280	-1     -280
2     140	-2     -140
4     70	-4     -70
5     56	-5     -56
7     40	-7     -40
8     35	-8     -35
10     28	-10     -28
14     20	-14     -20

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 43 }$

PRODUCT = 280 and SUM = 43
1     280	-1     -280
2     140	-2     -140
4     70	-4     -70
5     56	-5     -56
7     40	-7     -40
8     35	-8     -35
10     28	-10     -28
14     20	-14     -20

Step 6: Replace middle term $ 43 x $ with $ 35x+8x $:

$$ 10x^{2}+43x+28 = 10x^{2}+35x+8x+28 $$

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

$$ 10x^{2}+35x+8x+28 = 5x\left(2x+7\right) + 4\left(2x+7\right) = \left(5x+4\right) \left(2x+7\right) $$

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