8y^2-6y+9-12y^2-6y+5=

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Solution for 8y^2-6y+9-12y^2-6y+5= equation: 


Simplifying
8y2 + -6y + 9 + -12y2 + -6y + 5 = 0

Reorder the terms:
9 + 5 + -6y + -6y + 8y2 + -12y2 = 0

Combine like terms: 9 + 5 = 14
14 + -6y + -6y + 8y2 + -12y2 = 0

Combine like terms: -6y + -6y = -12y
14 + -12y + 8y2 + -12y2 = 0

Combine like terms: 8y2 + -12y2 = -4y2
14 + -12y + -4y2 = 0

Solving
14 + -12y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -6y + -2y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -6y + -2y2)' equal to zero and attempt to solve:

Simplifying
7 + -6y + -2y2 = 0

Solving
7 + -6y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3.5 + 3y + y2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 3y + 3.5 + y2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 3y + y2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 3y + y2 = 0 + 3.5
3y + y2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
3y + y2 = 3.5

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 3.5 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 3.5 + 2.25

Combine like terms: 3.5 + 2.25 = 5.75
2.25 + 3y + y2 = 5.75

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(y + 1.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
y + 1.5 = 2.397915762

Simplifying
y + 1.5 = 2.397915762

Reorder the terms:
1.5 + y = 2.397915762

Solving
1.5 + y = 2.397915762

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 2.397915762 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 2.397915762 + -1.5
y = 2.397915762 + -1.5

Combine like terms: 2.397915762 + -1.5 = 0.897915762
y = 0.897915762

Simplifying
y = 0.897915762


Subproblem 2
y + 1.5 = -2.397915762

Simplifying
y + 1.5 = -2.397915762

Reorder the terms:
1.5 + y = -2.397915762

Solving
1.5 + y = -2.397915762

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -2.397915762 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -2.397915762 + -1.5
y = -2.397915762 + -1.5

Combine like terms: -2.397915762 + -1.5 = -3.897915762
y = -3.897915762

Simplifying
y = -3.897915762


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.897915762, -3.897915762}
Solution
y = {0.897915762, -3.897915762}

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