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:

$$ a = 30 , b = -1 ~ \text{ and } ~ c = -20 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 30 }$ by the constant term $\color{blue}{c = -20} $.

$$ a \cdot c = -600 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -600 $ and add to $ b = -1 $.

Step 4: All pairs of numbers with a product of $ -600 $ are:

PRODUCT = -600
-1     600	1     -600
-2     300	2     -300
-3     200	3     -200
-4     150	4     -150
-5     120	5     -120
-6     100	6     -100
-8     75	8     -75
-10     60	10     -60
-12     50	12     -50
-15     40	15     -40
-20     30	20     -30
-24     25	24     -25

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -1 }$

PRODUCT = -600 and SUM = -1
-1     600	1     -600
-2     300	2     -300
-3     200	3     -200
-4     150	4     -150
-5     120	5     -120
-6     100	6     -100
-8     75	8     -75
-10     60	10     -60
-12     50	12     -50
-15     40	15     -40
-20     30	20     -30
-24     25	24     -25

Step 6: Replace middle term $ -1 x $ with $ 24x-25x $:

$$ 30x^{2}-x-20 = 30x^{2}+24x-25x-20 $$

Step 7: Apply factoring by grouping. Factor $ 6x $ out of the first two terms and $ -5 $ out of the last two terms.

$$ 30x^{2}+24x-25x-20 = 6x\left(5x+4\right) -5\left(5x+4\right) = \left(6x-5\right) \left(5x+4\right) $$

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