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:

$$ a = 6 , b = 43 ~ \text{ and } ~ c = 7 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 6 }$ by the constant term $\color{blue}{c = 7} $.

$$ a \cdot c = 42 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 42 $ and add to $ b = 43 $.

Step 4: All pairs of numbers with a product of $ 42 $ are:

PRODUCT = 42
1     42	-1     -42
2     21	-2     -21
3     14	-3     -14
6     7	-6     -7

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

PRODUCT = 42 and SUM = 43
1     42	-1     -42
2     21	-2     -21
3     14	-3     -14
6     7	-6     -7

Step 6: Replace middle term $ 43 x $ with $ 42x+x $:

$$ 6x^{2}+43x+7 = 6x^{2}+42x+x+7 $$

Step 7: Apply factoring by grouping. Factor $ 6x $ out of the first two terms and $ 1 $ out of the last two terms.

$$ 6x^{2}+42x+x+7 = 6x\left(x+7\right) + 1\left(x+7\right) = \left(6x+1\right) \left(x+7\right) $$

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