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:

$$ a = 18 , b = -77 ~ \text{ and } ~ c = -18 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 18 }$ by the constant term $\color{blue}{c = -18} $.

$$ a \cdot c = -324 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -324 $ and add to $ b = -77 $.

Step 4: All pairs of numbers with a product of $ -324 $ are:

PRODUCT = -324
-1     324	1     -324
-2     162	2     -162
-3     108	3     -108
-4     81	4     -81
-6     54	6     -54
-9     36	9     -36
-12     27	12     -27
-18     18	18     -18

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -77 }$

PRODUCT = -324 and SUM = -77
-1     324	1     -324
-2     162	2     -162
-3     108	3     -108
-4     81	4     -81
-6     54	6     -54
-9     36	9     -36
-12     27	12     -27
-18     18	18     -18

Step 6: Replace middle term $ -77 x $ with $ 4x-81x $:

$$ 18x^{2}-77x-18 = 18x^{2}+4x-81x-18 $$

Step 7: Apply factoring by grouping. Factor $ 2x $ out of the first two terms and $ -9 $ out of the last two terms.

$$ 18x^{2}+4x-81x-18 = 2x\left(9x+2\right) -9\left(9x+2\right) = \left(2x-9\right) \left(9x+2\right) $$

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