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:

$$ \color{blue}{ b = -19 } ~ \text{ and } ~ \color{red}{ c = -150 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -19 } $ and multiply to $ \color{red}{ -150 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -150 }$.

PRODUCT = -150
-1     150	1     -150
-2     75	2     -75
-3     50	3     -50
-5     30	5     -30
-6     25	6     -25
-10     15	10     -15

Step 3: Find out which pair sums up to $\color{blue}{ b = -19 }$

PRODUCT = -150 and SUM = -19
-1     150	1     -150
-2     75	2     -75
-3     50	3     -50
-5     30	5     -30
-6     25	6     -25
-10     15	10     -15

Step 4: Put 6 and -25 into placeholders to get factored form.

$$ \begin{aligned} y^{2}-19y-150 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ y^{2}-19y-150 & = (x + 6)(x -25) \end{aligned} $$

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