8y^2-9y+6-11y^2-9y+3=

Solution for 8y^2-9y+6-11y^2-9y+3= equation:

Simplifying
8y2 + -9y + 6 + -11y2 + -9y + 3 = 0

Reorder the terms:
6 + 3 + -9y + -9y + 8y2 + -11y2 = 0

Combine like terms: 6 + 3 = 9
9 + -9y + -9y + 8y2 + -11y2 = 0

Combine like terms: -9y + -9y = -18y
9 + -18y + 8y2 + -11y2 = 0

Combine like terms: 8y2 + -11y2 = -3y2
9 + -18y + -3y2 = 0

Solving
9 + -18y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -6y + -1y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -6y + -1y2)' equal to zero and attempt to solve:

Simplifying
3 + -6y + -1y2 = 0

Solving
3 + -6y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + 6y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 6y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6y + y2 = 0 + 3
6y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
6y + y2 = 3

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 3 + 9

Reorder the terms:
9 + 6y + y2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6y + y2 = 12

Factor a perfect square on the left side:
(y + 3)(y + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(y + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1
y + 3 = 3.464101615

Simplifying
y + 3 = 3.464101615

Reorder the terms:
3 + y = 3.464101615

Solving
3 + y = 3.464101615

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + y = 3.464101615 + -3
y = 3.464101615 + -3

Combine like terms: 3.464101615 + -3 = 0.464101615
y = 0.464101615

Simplifying
y = 0.464101615

Subproblem 2
y + 3 = -3.464101615

Simplifying
y + 3 = -3.464101615

Reorder the terms:
3 + y = -3.464101615

Solving
3 + y = -3.464101615

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -3.464101615 + -3

Combine like terms: 3 + -3 = 0
0 + y = -3.464101615 + -3
y = -3.464101615 + -3

Combine like terms: -3.464101615 + -3 = -6.464101615
y = -6.464101615

Simplifying
y = -6.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.464101615, -6.464101615}
Solution
y = {0.464101615, -6.464101615}