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:

$$ a = 3 , b = -14 ~ \text{ and } ~ c = 15 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 15} $.

$$ a \cdot c = 45 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 45 $ and add to $ b = -14 $.

Step 4: All pairs of numbers with a product of $ 45 $ are:

PRODUCT = 45
1     45	-1     -45
3     15	-3     -15
5     9	-5     -9

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -14 }$

PRODUCT = 45 and SUM = -14
1     45	-1     -45
3     15	-3     -15
5     9	-5     -9

Step 6: Replace middle term $ -14 x $ with $ -5x-9x $:

$$ 3x^{2}-14x+15 = 3x^{2}-5x-9x+15 $$

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

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

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