8w^2-6w-9=0

Solution for 8w^2-6w-9=0 equation:

Simplifying
8w2 + -6w + -9 = 0

Reorder the terms:
-9 + -6w + 8w2 = 0

Solving
-9 + -6w + 8w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -4w)(3 + -2w) = 0

Subproblem 1
Set the factor '(-3 + -4w)' equal to zero and attempt to solve:

Simplifying
-3 + -4w = 0

Solving
-3 + -4w = 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 + -4w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4w = 0 + 3
-4w = 0 + 3

Combine like terms: 0 + 3 = 3
-4w = 3

Divide each side by '-4'.
w = -0.75

Simplifying
w = -0.75
Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-0.75, 1.5}