Step 1 :

After factoring out $ -1 $ we have:

$$ -16x^{2}+383x+24 = - ~ ( 16x^{2}-383x-24 ) $$

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:

$$ a = 16 , b = -383 ~ \text{ and } ~ c = -24 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 16 }$ by the constant term $\color{blue}{c = -24} $.

$$ a \cdot c = -384 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -384 $ and add to $ b = -383 $.

Step 5: All pairs of numbers with a product of $ -384 $ are:

PRODUCT = -384
-1     384	1     -384
-2     192	2     -192
-3     128	3     -128
-4     96	4     -96
-6     64	6     -64
-8     48	8     -48
-12     32	12     -32
-16     24	16     -24

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -383 }$

PRODUCT = -384 and SUM = -383
-1     384	1     -384
-2     192	2     -192
-3     128	3     -128
-4     96	4     -96
-6     64	6     -64
-8     48	8     -48
-12     32	12     -32
-16     24	16     -24

Step 7: Replace middle term $ -383 x $ with $ x-384x $:

$$ 16x^{2}-383x-24 = 16x^{2}+x-384x-24 $$

Step 8: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -24 $ out of the last two terms.

$$ 16x^{2}+x-384x-24 = x\left(16x+1\right) -24\left(16x+1\right) = \left(x-24\right) \left(16x+1\right) $$

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