2y^2-8y+9-12y^2-8y+3=

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Solution for 2y^2-8y+9-12y^2-8y+3= equation:


Simplifying
2y2 + -8y + 9 + -12y2 + -8y + 3 = 0

Reorder the terms:
9 + 3 + -8y + -8y + 2y2 + -12y2 = 0

Combine like terms: 9 + 3 = 12
12 + -8y + -8y + 2y2 + -12y2 = 0

Combine like terms: -8y + -8y = -16y
12 + -16y + 2y2 + -12y2 = 0

Combine like terms: 2y2 + -12y2 = -10y2
12 + -16y + -10y2 = 0

Solving
12 + -16y + -10y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -8y + -5y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(6 + -8y + -5y2)' equal to zero and attempt to solve:

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

Solving
6 + -8y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.2 + 1.6y + y2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 1.6y + 1.2 + y2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 1.6y + y2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 1.6y + y2 = 0 + 1.2
1.6y + y2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
1.6y + y2 = 1.2

The y term is 1.6y.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6y + 0.64 + y2 = 1.2 + 0.64

Reorder the terms:
0.64 + 1.6y + y2 = 1.2 + 0.64

Combine like terms: 1.2 + 0.64 = 1.84
0.64 + 1.6y + y2 = 1.84

Factor a perfect square on the left side:
(y + 0.8)(y + 0.8) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(y + 0.8) equal to 1.356465997 and -1.356465997.


Subproblem 1
y + 0.8 = 1.356465997

Simplifying
y + 0.8 = 1.356465997

Reorder the terms:
0.8 + y = 1.356465997

Solving
0.8 + y = 1.356465997

Solving for variable 'y'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + y = 1.356465997 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + y = 1.356465997 + -0.8
y = 1.356465997 + -0.8

Combine like terms: 1.356465997 + -0.8 = 0.556465997
y = 0.556465997

Simplifying
y = 0.556465997


Subproblem 2
y + 0.8 = -1.356465997

Simplifying
y + 0.8 = -1.356465997

Reorder the terms:
0.8 + y = -1.356465997

Solving
0.8 + y = -1.356465997

Solving for variable 'y'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + y = -1.356465997 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + y = -1.356465997 + -0.8
y = -1.356465997 + -0.8

Combine like terms: -1.356465997 + -0.8 = -2.156465997
y = -2.156465997

Simplifying
y = -2.156465997


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.556465997, -2.156465997}
Solution
y = {0.556465997, -2.156465997}

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