Hell . what are the solutions to `10x^2 - 38x - 8 = 0`? is this when i find the factors and use the numbers within the factors to determine the zeros? i hope that made sense lol

x = -⅕; x = 4  

Step-by-step explanation:

Yes, this when you find the factors and use the numbers within the factors to determine the zeros

Here's one way to do it.

Step 1. Factor out the highest common factor of all three terms.

You can factor out a 2.

10x² - 38x - 8 = 0      Divide each side by 2

5x² -  19x - 4 = 0

Step 2. Multiply the leading coefficient and the constant

5 × (-4) = -20

Step 3. List the factors of -20 that will add to give the coefficient of x:

The factors are 1 and -20: 1 – 20 = -19

Step 4. Rewrite the equation in four terms

Split the middle term, using the factors from Step 3.

5x² + x - 20x - 4  = 0

Step 5. Factor by grouping

x(5x+1) – 4(5x +1) = (x – 4)(5x + 1)  

Step 6. Find the zeros

(x – 4)(5x + 1) = 0

x - 4 = 0     5x+1 = 0

    x = 4         5x = -1

                       x = -⅕

The zeros are at x = -⅕ and x = 4.