(8w^2)-19w-15=0

Solution for (8w^2)-19w-15=0 equation:

Simplifying
(8w2) + -19w + -15 = 0

Reorder the terms:
-15 + -19w + (8w2) = 0

Solving
-15 + -19w + (8w2) = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -8w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-5 + -8w)' equal to zero and attempt to solve:

Simplifying
-5 + -8w = 0

Solving
-5 + -8w = 0

Move all terms containing w to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + -8w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8w = 0 + 5
-8w = 0 + 5

Combine like terms: 0 + 5 = 5
-8w = 5

Divide each side by '-8'.
w = -0.625

Simplifying
w = -0.625
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-0.625, 3}