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:

$$ a = 30 , b = -29 ~ \text{ and } ~ c = -45 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 30 }$ by the constant term $\color{blue}{c = -45} $.

$$ a \cdot c = -1350 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -1350 $ and add to $ b = -29 $.

Step 4: All pairs of numbers with a product of $ -1350 $ are:

PRODUCT = -1350
-1     1350	1     -1350
-2     675	2     -675
-3     450	3     -450
-5     270	5     -270
-6     225	6     -225
-9     150	9     -150
-10     135	10     -135
-15     90	15     -90
-18     75	18     -75
-25     54	25     -54
-27     50	27     -50
-30     45	30     -45

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -29 }$

PRODUCT = -1350 and SUM = -29
-1     1350	1     -1350
-2     675	2     -675
-3     450	3     -450
-5     270	5     -270
-6     225	6     -225
-9     150	9     -150
-10     135	10     -135
-15     90	15     -90
-18     75	18     -75
-25     54	25     -54
-27     50	27     -50
-30     45	30     -45

Step 6: Replace middle term $ -29 x $ with $ 25x-54x $:

$$ 30x^{2}-29x-45 = 30x^{2}+25x-54x-45 $$

Step 7: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -9 $ out of the last two terms.

$$ 30x^{2}+25x-54x-45 = 5x\left(6x+5\right) -9\left(6x+5\right) = \left(5x-9\right) \left(6x+5\right) $$

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