6Y^2-9Y-6=0

Solution for 6Y^2-9Y-6=0 equation:

Simplifying
6Y2 + -9Y + -6 = 0

Reorder the terms:
-6 + -9Y + 6Y2 = 0

Solving
-6 + -9Y + 6Y2 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -3Y + 2Y2) = 0

Factor a trinomial.
3((-1 + -2Y)(2 + -1Y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -2Y)' equal to zero and attempt to solve:

Simplifying
-1 + -2Y = 0

Solving
-1 + -2Y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2Y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2Y = 0 + 1
-2Y = 0 + 1

Combine like terms: 0 + 1 = 1
-2Y = 1

Divide each side by '-2'.
Y = -0.5

Simplifying
Y = -0.5
Subproblem 2
Set the factor '(2 + -1Y)' equal to zero and attempt to solve:

Simplifying
2 + -1Y = 0

Solving
2 + -1Y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1Y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1Y = 0 + -2
-1Y = 0 + -2

Combine like terms: 0 + -2 = -2
-1Y = -2

Divide each side by '-1'.
Y = 2

Simplifying
Y = 2
Solution
Y = {-0.5, 2}