Step 1 :

After factoring out $ 4 $ we have:

$$ 4w^{2}-52w-120 = 4 ( w^{2}-13w-30 ) $$

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:

$$ \color{blue}{ b = -13 } ~ \text{ and } ~ \color{red}{ c = -30 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -13 } $ and multiply to $ \color{red}{ -30 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -30 }$.

PRODUCT = -30
-1     30	1     -30
-2     15	2     -15
-3     10	3     -10
-5     6	5     -6

Step 4: Find out which pair sums up to $\color{blue}{ b = -13 }$

PRODUCT = -30 and SUM = -13
-1     30	1     -30
-2     15	2     -15
-3     10	3     -10
-5     6	5     -6

Step 5: Put 2 and -15 into placeholders to get factored form.

$$ \begin{aligned} w^{2}-13w-30 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ w^{2}-13w-30 & = (x + 2)(x -15) \end{aligned} $$

Polynomial Factoring Calculator