Step 1 :

After factoring out $ 5 $ we have:

$$ 10y^{2}+5y-180 = 5 ( 2y^{2}+y-36 ) $$

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:

$$ a = 2 , b = 1 ~ \text{ and } ~ c = -36 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -36} $.

$$ a \cdot c = -72 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -72 $ and add to $ b = 1 $.

Step 5: All pairs of numbers with a product of $ -72 $ are:

PRODUCT = -72
-1     72	1     -72
-2     36	2     -36
-3     24	3     -24
-4     18	4     -18
-6     12	6     -12
-8     9	8     -9

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 1 }$

PRODUCT = -72 and SUM = 1
-1     72	1     -72
-2     36	2     -36
-3     24	3     -24
-4     18	4     -18
-6     12	6     -12
-8     9	8     -9

Step 7: Replace middle term $ 1 x $ with $ 9x-8x $:

$$ 2x^{2}+x-36 = 2x^{2}+9x-8x-36 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 2x^{2}+9x-8x-36 = x\left(2x+9\right) -4\left(2x+9\right) = \left(x-4\right) \left(2x+9\right) $$

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