Step 1 :

After factoring out $ 6x $ we have:

$$ 18x^{3}-120x^{2}-42x = 6x ( 3x^{2}-20x-7 ) $$

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:

$$ a = 3 , b = -20 ~ \text{ and } ~ c = -7 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = -7} $.

$$ a \cdot c = -21 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -21 $ and add to $ b = -20 $.

Step 5: All pairs of numbers with a product of $ -21 $ are:

PRODUCT = -21
-1     21	1     -21
-3     7	3     -7

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -20 }$

PRODUCT = -21 and SUM = -20
-1     21	1     -21
-3     7	3     -7

Step 7: Replace middle term $ -20 x $ with $ x-21x $:

$$ 3x^{2}-20x-7 = 3x^{2}+x-21x-7 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -7 $ out of the last two terms.

$$ 3x^{2}+x-21x-7 = x\left(3x+1\right) -7\left(3x+1\right) = \left(x-7\right) \left(3x+1\right) $$

Polynomial Factoring Calculator