Step 1: 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:

$$ \color{blue}{ b = -12 } ~ \text{ and } ~ \color{red}{ c = -13 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -12 } $ and multiply to $ \color{red}{ -13 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -13 }$.

PRODUCT = -13
-1     13	1     -13

Step 3: Find out which pair sums up to $\color{blue}{ b = -12 }$

PRODUCT = -13 and SUM = -12
-1     13	1     -13

Step 4: Put 1 and -13 into placeholders to get factored form.

$$ \begin{aligned} s^{2}-12s-13 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ s^{2}-12s-13 & = (x + 1)(x -13) \end{aligned} $$

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