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:

$$ a = 3 , b = -145 ~ \text{ and } ~ c = 450 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 3 }$ by the constant term $\color{blue}{c = 450} $.

$$ a \cdot c = 1350 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 1350 $ and add to $ b = -145 $.

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 $\color{blue}{ b = -145 }$

PRODUCT = 1350 and SUM = -145
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 $ -145 x $ with $ -10x-135x $:

$$ 3x^{2}-145x+450 = 3x^{2}-10x-135x+450 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -45 $ out of the last two terms.

$$ 3x^{2}-10x-135x+450 = x\left(3x-10\right) -45\left(3x-10\right) = \left(x-45\right) \left(3x-10\right) $$

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