Step 1 :

After factoring out $ 6 $ we have:

$$ 48m^{2}+150m-168 = 6 ( 8m^{2}+25m-28 ) $$

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:

$$ a = 8 , b = 25 ~ \text{ and } ~ c = -28 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = -28} $.

$$ a \cdot c = -224 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -224 $ and add to $ b = 25 $.

Step 5: All pairs of numbers with a product of $ -224 $ are:

PRODUCT = -224
-1     224	1     -224
-2     112	2     -112
-4     56	4     -56
-7     32	7     -32
-8     28	8     -28
-14     16	14     -16

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 25 }$

PRODUCT = -224 and SUM = 25
-1     224	1     -224
-2     112	2     -112
-4     56	4     -56
-7     32	7     -32
-8     28	8     -28
-14     16	14     -16

Step 7: Replace middle term $ 25 x $ with $ 32x-7x $:

$$ 8x^{2}+25x-28 = 8x^{2}+32x-7x-28 $$

Step 8: Apply factoring by grouping. Factor $ 8x $ out of the first two terms and $ -7 $ out of the last two terms.

$$ 8x^{2}+32x-7x-28 = 8x\left(x+4\right) -7\left(x+4\right) = \left(8x-7\right) \left(x+4\right) $$

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