Factor polynomial $$ -14x^{2}+13x-3 $$

$$ -14x^{2}+13x-3 = -( 2x-1 )( 7x-3 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -14x^{2}+13x-3 = - ~ ( 14x^{2}-13x+3 ) $$

Step 2 :

Step 2: 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:

$$ a = 14 , b = -13 ~ \text{ and } ~ c = 3 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 14 }$ by the constant term $\color{blue}{c = 3} $.

$$ a \cdot c = 42 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = 42 $ and add to $ b = -13 $.

Step 5: 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 6: Find out which factor pair sums up to $\color{blue}{ b = -13 }$

PRODUCT = 42 and SUM = -13
1     42	-1     -42
2     21	-2     -21
3     14	-3     -14
6     7	-6     -7

Step 7: Replace middle term $ -13 x $ with $ -6x-7x $:

$$ 14x^{2}-13x+3 = 14x^{2}-6x-7x+3 $$

Step 8: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ -1 $ out of the last two terms.

$$ 14x^{2}-6x-7x+3 = 2x\left(7x-3\right) -1\left(7x-3\right) = \left(2x-1\right) \left(7x-3\right) $$

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