[-(y^4-y^2+1)-(y^4+7y^2+1)]+(6y^4-9y^2-12)=

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Solution for [-(y^4-y^2+1)-(y^4+7y^2+1)]+(6y^4-9y^2-12)= equation: 


Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 7y2 + 1)] + (6y4 + -9y2 + -12) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 7y2 + 1)] + (6y4 + -9y2 + -12) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 7y2 + 1)] + (6y4 + -9y2 + -12) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 7y2 + 1)] + (6y4 + -9y2 + -12) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 7y2 + y4)] + (6y4 + -9y2 + -12) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 7y2 * -1 + y4 * -1)] + (6y4 + -9y2 + -12) = 0
[-1 + 1y2 + -1y4 + (-1 + -7y2 + -1y4)] + (6y4 + -9y2 + -12) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -7y2 + -1y4 + -1y4] + (6y4 + -9y2 + -12) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -7y2 + -1y4 + -1y4] + (6y4 + -9y2 + -12) = 0

Combine like terms: 1y2 + -7y2 = -6y2
[-2 + -6y2 + -1y4 + -1y4] + (6y4 + -9y2 + -12) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -6y2 + -2y4] + (6y4 + -9y2 + -12) = 0

Remove brackets around [-2 + -6y2 + -2y4]
-2 + -6y2 + -2y4 + (6y4 + -9y2 + -12) = 0

Reorder the terms:
-2 + -6y2 + -2y4 + (-12 + -9y2 + 6y4) = 0

Remove parenthesis around (-12 + -9y2 + 6y4)
-2 + -6y2 + -2y4 + -12 + -9y2 + 6y4 = 0

Reorder the terms:
-2 + -12 + -6y2 + -9y2 + -2y4 + 6y4 = 0

Combine like terms: -2 + -12 = -14
-14 + -6y2 + -9y2 + -2y4 + 6y4 = 0

Combine like terms: -6y2 + -9y2 = -15y2
-14 + -15y2 + -2y4 + 6y4 = 0

Combine like terms: -2y4 + 6y4 = 4y4
-14 + -15y2 + 4y4 = 0

Solving
-14 + -15y2 + 4y4 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
-3.5 + -3.75y2 + y4 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -3.75y2 + 3.5 + y4 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -3.75y2 + y4 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -3.75y2 + y4 = 0 + 3.5
-3.75y2 + y4 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-3.75y2 + y4 = 3.5

The y term is -3.75y2.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75y2 + 3.515625 + y4 = 3.5 + 3.515625

Reorder the terms:
3.515625 + -3.75y2 + y4 = 3.5 + 3.515625

Combine like terms: 3.5 + 3.515625 = 7.015625
3.515625 + -3.75y2 + y4 = 7.015625

Factor a perfect square on the left side:
(y2 + -1.875)(y2 + -1.875) = 7.015625

Calculate the square root of the right side: 2.648702513

Break this problem into two subproblems by setting 
(y2 + -1.875) equal to 2.648702513 and -2.648702513.


Subproblem 1
y2 + -1.875 = 2.648702513

Simplifying
y2 + -1.875 = 2.648702513

Reorder the terms:
-1.875 + y2 = 2.648702513

Solving
-1.875 + y2 = 2.648702513

Solving for variable 'y'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + y2 = 2.648702513 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + y2 = 2.648702513 + 1.875
y2 = 2.648702513 + 1.875

Combine like terms: 2.648702513 + 1.875 = 4.523702513
y2 = 4.523702513

Simplifying
y2 = 4.523702513

Take the square root of each side:
y = {-2.126899742, 2.126899742}


Subproblem 2
y2 + -1.875 = -2.648702513

Simplifying
y2 + -1.875 = -2.648702513

Reorder the terms:
-1.875 + y2 = -2.648702513

Solving
-1.875 + y2 = -2.648702513

Solving for variable 'y'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + y2 = -2.648702513 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + y2 = -2.648702513 + 1.875
y2 = -2.648702513 + 1.875

Combine like terms: -2.648702513 + 1.875 = -0.773702513
y2 = -0.773702513

Simplifying
y2 = -0.773702513

Reorder the terms:
0.773702513 + y2 = -0.773702513 + 0.773702513

Combine like terms: -0.773702513 + 0.773702513 = 0.000000000
0.773702513 + y2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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