Factor polynomial $$ 9x^{2}+49x-30 $$

$$ 9x^{2}+49x-30 = ( 9x-5 )( x+6 ) $$

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:

$$ a = 9 , b = 49 ~ \text{ and } ~ c = -30 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = -30} $.

$$ a \cdot c = -270 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -270 $ and add to $ b = 49 $.

Step 4: All pairs of numbers with a product of $ -270 $ are:

PRODUCT = -270
-1     270	1     -270
-2     135	2     -135
-3     90	3     -90
-5     54	5     -54
-6     45	6     -45
-9     30	9     -30
-10     27	10     -27
-15     18	15     -18

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 49 }$

PRODUCT = -270 and SUM = 49
-1     270	1     -270
-2     135	2     -135
-3     90	3     -90
-5     54	5     -54
-6     45	6     -45
-9     30	9     -30
-10     27	10     -27
-15     18	15     -18

Step 6: Replace middle term $ 49 x $ with $ 54x-5x $:

$$ 9x^{2}+49x-30 = 9x^{2}+54x-5x-30 $$

Step 7: Apply factoring by grouping. Factor $ 9x $ out of the first two terms and $ -5 $ out of the last two terms.

$$ 9x^{2}+54x-5x-30 = 9x\left(x+6\right) -5\left(x+6\right) = \left(9x-5\right) \left(x+6\right) $$

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