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:

$$ a = 12 , b = -29 ~ \text{ and } ~ c = 15 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 12 }$ by the constant term $\color{blue}{c = 15} $.

$$ a \cdot c = 180 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 180 $ and add to $ b = -29 $.

Step 4: All pairs of numbers with a product of $ 180 $ are:

PRODUCT = 180
1     180	-1     -180
2     90	-2     -90
3     60	-3     -60
4     45	-4     -45
5     36	-5     -36
6     30	-6     -30
9     20	-9     -20
10     18	-10     -18
12     15	-12     -15

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

PRODUCT = 180 and SUM = -29
1     180	-1     -180
2     90	-2     -90
3     60	-3     -60
4     45	-4     -45
5     36	-5     -36
6     30	-6     -30
9     20	-9     -20
10     18	-10     -18
12     15	-12     -15

Step 6: Replace middle term $ -29 x $ with $ -9x-20x $:

$$ 12x^{2}-29x+15 = 12x^{2}-9x-20x+15 $$

Step 7: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ -5 $ out of the last two terms.

$$ 12x^{2}-9x-20x+15 = 3x\left(4x-3\right) -5\left(4x-3\right) = \left(3x-5\right) \left(4x-3\right) $$

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