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:

$$ a = 30 , b = -11 ~ \text{ and } ~ c = -30 $$

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

$$ a \cdot c = -900 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -900 $ and add to $ b = -11 $.

Step 4: All pairs of numbers with a product of $ -900 $ are:

PRODUCT = -900
-1     900	1     -900
-2     450	2     -450
-3     300	3     -300
-4     225	4     -225
-5     180	5     -180
-6     150	6     -150
-9     100	9     -100
-10     90	10     -90
-12     75	12     -75
-15     60	15     -60
-18     50	18     -50
-20     45	20     -45
-25     36	25     -36
-30     30	30     -30

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -11 }$

PRODUCT = -900 and SUM = -11
-1     900	1     -900
-2     450	2     -450
-3     300	3     -300
-4     225	4     -225
-5     180	5     -180
-6     150	6     -150
-9     100	9     -100
-10     90	10     -90
-12     75	12     -75
-15     60	15     -60
-18     50	18     -50
-20     45	20     -45
-25     36	25     -36
-30     30	30     -30

Step 6: Replace middle term $ -11 x $ with $ 25x-36x $:

$$ 30x^{2}-11x-30 = 30x^{2}+25x-36x-30 $$

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

$$ 30x^{2}+25x-36x-30 = 5x\left(6x+5\right) -6\left(6x+5\right) = \left(5x-6\right) \left(6x+5\right) $$

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