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:

$$ a = 4 , b = -115 ~ \text{ and } ~ c = 375 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 4 }$ by the constant term $\color{blue}{c = 375} $.

$$ a \cdot c = 1500 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = 1500 $ and add to $ b = -115 $.

Step 4: All pairs of numbers with a product of $ 1500 $ are:

PRODUCT = 1500
1     1500	-1     -1500
2     750	-2     -750
3     500	-3     -500
4     375	-4     -375
5     300	-5     -300
6     250	-6     -250
10     150	-10     -150
12     125	-12     -125
15     100	-15     -100
20     75	-20     -75
25     60	-25     -60
30     50	-30     -50

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -115 }$

PRODUCT = 1500 and SUM = -115
1     1500	-1     -1500
2     750	-2     -750
3     500	-3     -500
4     375	-4     -375
5     300	-5     -300
6     250	-6     -250
10     150	-10     -150
12     125	-12     -125
15     100	-15     -100
20     75	-20     -75
25     60	-25     -60
30     50	-30     -50

Step 6: Replace middle term $ -115 x $ with $ -15x-100x $:

$$ 4x^{2}-115x+375 = 4x^{2}-15x-100x+375 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -25 $ out of the last two terms.

$$ 4x^{2}-15x-100x+375 = x\left(4x-15\right) -25\left(4x-15\right) = \left(x-25\right) \left(4x-15\right) $$

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