[-(y^4-y^2+1)-(y^4+8y^2+1)]+(4y^4-4y^2-3)=

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Solution for [-(y^4-y^2+1)-(y^4+8y^2+1)]+(4y^4-4y^2-3)= equation: 


Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 8y2 + 1)] + (4y4 + -4y2 + -3) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 8y2 + 1)] + (4y4 + -4y2 + -3) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 8y2 + 1)] + (4y4 + -4y2 + -3) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 8y2 + 1)] + (4y4 + -4y2 + -3) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 8y2 + y4)] + (4y4 + -4y2 + -3) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 8y2 * -1 + y4 * -1)] + (4y4 + -4y2 + -3) = 0
[-1 + 1y2 + -1y4 + (-1 + -8y2 + -1y4)] + (4y4 + -4y2 + -3) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -8y2 + -1y4 + -1y4] + (4y4 + -4y2 + -3) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -8y2 + -1y4 + -1y4] + (4y4 + -4y2 + -3) = 0

Combine like terms: 1y2 + -8y2 = -7y2
[-2 + -7y2 + -1y4 + -1y4] + (4y4 + -4y2 + -3) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -7y2 + -2y4] + (4y4 + -4y2 + -3) = 0

Remove brackets around [-2 + -7y2 + -2y4]
-2 + -7y2 + -2y4 + (4y4 + -4y2 + -3) = 0

Reorder the terms:
-2 + -7y2 + -2y4 + (-3 + -4y2 + 4y4) = 0

Remove parenthesis around (-3 + -4y2 + 4y4)
-2 + -7y2 + -2y4 + -3 + -4y2 + 4y4 = 0

Reorder the terms:
-2 + -3 + -7y2 + -4y2 + -2y4 + 4y4 = 0

Combine like terms: -2 + -3 = -5
-5 + -7y2 + -4y2 + -2y4 + 4y4 = 0

Combine like terms: -7y2 + -4y2 = -11y2
-5 + -11y2 + -2y4 + 4y4 = 0

Combine like terms: -2y4 + 4y4 = 2y4
-5 + -11y2 + 2y4 = 0

Solving
-5 + -11y2 + 2y4 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-2.5 + -5.5y2 + y4 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -5.5y2 + 2.5 + y4 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -5.5y2 + y4 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -5.5y2 + y4 = 0 + 2.5
-5.5y2 + y4 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-5.5y2 + y4 = 2.5

The y term is -5.5y2.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5y2 + 7.5625 + y4 = 2.5 + 7.5625

Reorder the terms:
7.5625 + -5.5y2 + y4 = 2.5 + 7.5625

Combine like terms: 2.5 + 7.5625 = 10.0625
7.5625 + -5.5y2 + y4 = 10.0625

Factor a perfect square on the left side:
(y2 + -2.75)(y2 + -2.75) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(y2 + -2.75) equal to 3.172144385 and -3.172144385.


Subproblem 1
y2 + -2.75 = 3.172144385

Simplifying
y2 + -2.75 = 3.172144385

Reorder the terms:
-2.75 + y2 = 3.172144385

Solving
-2.75 + y2 = 3.172144385

Solving for variable 'y'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + y2 = 3.172144385 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + y2 = 3.172144385 + 2.75
y2 = 3.172144385 + 2.75

Combine like terms: 3.172144385 + 2.75 = 5.922144385
y2 = 5.922144385

Simplifying
y2 = 5.922144385

Take the square root of each side:
y = {-2.433545641, 2.433545641}


Subproblem 2
y2 + -2.75 = -3.172144385

Simplifying
y2 + -2.75 = -3.172144385

Reorder the terms:
-2.75 + y2 = -3.172144385

Solving
-2.75 + y2 = -3.172144385

Solving for variable 'y'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + y2 = -3.172144385 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + y2 = -3.172144385 + 2.75
y2 = -3.172144385 + 2.75

Combine like terms: -3.172144385 + 2.75 = -0.422144385
y2 = -0.422144385

Simplifying
y2 = -0.422144385

Reorder the terms:
0.422144385 + y2 = -0.422144385 + 0.422144385

Combine like terms: -0.422144385 + 0.422144385 = 0.000000000
0.422144385 + 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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