Factor polynomial $$ 15x^{2}+16x-15 $$

$$ 15x^{2}+16x-15 = ( 5x-3 )( 3x+5 ) $$

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:

$$ a = 15 , b = 16 ~ \text{ and } ~ c = -15 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 15 }$ by the constant term $\color{blue}{c = -15} $.

$$ a \cdot c = -225 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -225 $ and add to $ b = 16 $.

Step 4: All pairs of numbers with a product of $ -225 $ are:

PRODUCT = -225
-1     225	1     -225
-3     75	3     -75
-5     45	5     -45
-9     25	9     -25
-15     15	15     -15

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 16 }$

PRODUCT = -225 and SUM = 16
-1     225	1     -225
-3     75	3     -75
-5     45	5     -45
-9     25	9     -25
-15     15	15     -15

Step 6: Replace middle term $ 16 x $ with $ 25x-9x $:

$$ 15x^{2}+16x-15 = 15x^{2}+25x-9x-15 $$

Step 7: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -3 $ out of the last two terms.

$$ 15x^{2}+25x-9x-15 = 5x\left(3x+5\right) -3\left(3x+5\right) = \left(5x-3\right) \left(3x+5\right) $$

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