Step 1 :

After factoring out $ -1 $ we have:

$$ -25x^{2}-196x+36 = - ~ ( 25x^{2}+196x-36 ) $$

Step 2 :

Step 2: 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:

$$ a = 25 , b = 196 ~ \text{ and } ~ c = -36 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 25 }$ by the constant term $\color{blue}{c = -36} $.

$$ a \cdot c = -900 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -900 $ and add to $ b = 196 $.

Step 5: All pairs of numbers with a product of $ -900 $ are:

PRODUCT = -900
-1     900	1     -900
-2     450	2     -450
-3     300	3     -300
-4     225	4     -225
-5     180	5     -180
-6     150	6     -150
-9     100	9     -100
-10     90	10     -90
-12     75	12     -75
-15     60	15     -60
-18     50	18     -50
-20     45	20     -45
-25     36	25     -36
-30     30	30     -30

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 196 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ 196 }$, we conclude the polynomial cannot be factored.

Polynomial Factoring Calculator