8y^2-6y-9=0

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

Simplifying
8y2 + -6y + -9 = 0

Reorder the terms:
-9 + -6y + 8y2 = 0

Solving
-9 + -6y + 8y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-3 + -4y = 0

Solving
-3 + -4y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4y = 0 + 3

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

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

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

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

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

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

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

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

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