Step 1 :

After factoring out $ 3 $ we have:

$$ 3m^{2}+66m-69 = 3 ( m^{2}+22m-23 ) $$

Step 2 :

Step 2: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = 22 } ~ \text{ and } ~ \color{red}{ c = -23 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 22 } $ and multiply to $ \color{red}{ -23 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -23 }$.

PRODUCT = -23
-1     23	1     -23

Step 4: Find out which pair sums up to $\color{blue}{ b = 22 }$

PRODUCT = -23 and SUM = 22
-1     23	1     -23

Step 5: Put -1 and 23 into placeholders to get factored form.

$$ \begin{aligned} m^{2}+22m-23 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ m^{2}+22m-23 & = (x -1)(x + 23) \end{aligned} $$

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