Step 1 :

After factoring out $ 2 $ we have:

$$ 26x^{2}+34x-36 = 2 ( 13x^{2}+17x-18 ) $$

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:

$$ a = 13 , b = 17 ~ \text{ and } ~ c = -18 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 13 }$ by the constant term $\color{blue}{c = -18} $.

$$ a \cdot c = -234 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -234 $ and add to $ b = 17 $.

Step 5: All pairs of numbers with a product of $ -234 $ are:

PRODUCT = -234
-1     234	1     -234
-2     117	2     -117
-3     78	3     -78
-6     39	6     -39
-9     26	9     -26
-13     18	13     -18

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 17 }$

PRODUCT = -234 and SUM = 17
-1     234	1     -234
-2     117	2     -117
-3     78	3     -78
-6     39	6     -39
-9     26	9     -26
-13     18	13     -18

Step 7: Replace middle term $ 17 x $ with $ 26x-9x $:

$$ 13x^{2}+17x-18 = 13x^{2}+26x-9x-18 $$

Step 8: Apply factoring by grouping. Factor $ 13x $ out of the first two terms and $ -9 $ out of the last two terms.

$$ 13x^{2}+26x-9x-18 = 13x\left(x+2\right) -9\left(x+2\right) = \left(13x-9\right) \left(x+2\right) $$

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