Factor polynomial $$ 28x^{2}+13x-6 $$

$$ 28x^{2}+13x-6 = ( 7x-2 )( 4x+3 ) $$

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:

$$ a = 28 , b = 13 ~ \text{ and } ~ c = -6 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 28 }$ by the constant term $\color{blue}{c = -6} $.

$$ a \cdot c = -168 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -168 $ and add to $ b = 13 $.

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 $\color{blue}{ b = 13 }$

PRODUCT = -168 and SUM = 13
-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 $ 13 x $ with $ 21x-8x $:

$$ 28x^{2}+13x-6 = 28x^{2}+21x-8x-6 $$

Step 7: Apply factoring by grouping. Factor $ 7x $ out of the first two terms and $ -2 $ out of the last two terms.

$$ 28x^{2}+21x-8x-6 = 7x\left(4x+3\right) -2\left(4x+3\right) = \left(7x-2\right) \left(4x+3\right) $$

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