Step 1 :

After factoring out $ -1 $ we have:

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

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:

$$ a = 3 , b = 1 ~ \text{ and } ~ c = -14 $$

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

$$ a \cdot c = -42 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -42 $ and add to $ b = 1 $.

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 $\color{blue}{ b = 1 }$

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

Step 7: Replace middle term $ 1 x $ with $ 7x-6x $:

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

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

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

Polynomial Factoring Calculator