[-(y^4-y^2+1)-(y^4+4y^2+1)]+(7y^4-5y^2-7)=

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Solution for [-(y^4-y^2+1)-(y^4+4y^2+1)]+(7y^4-5y^2-7)= equation: 


Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 4y2 + 1)] + (7y4 + -5y2 + -7) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 4y2 + 1)] + (7y4 + -5y2 + -7) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 4y2 + 1)] + (7y4 + -5y2 + -7) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 4y2 + 1)] + (7y4 + -5y2 + -7) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 4y2 + y4)] + (7y4 + -5y2 + -7) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 4y2 * -1 + y4 * -1)] + (7y4 + -5y2 + -7) = 0
[-1 + 1y2 + -1y4 + (-1 + -4y2 + -1y4)] + (7y4 + -5y2 + -7) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -4y2 + -1y4 + -1y4] + (7y4 + -5y2 + -7) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -4y2 + -1y4 + -1y4] + (7y4 + -5y2 + -7) = 0

Combine like terms: 1y2 + -4y2 = -3y2
[-2 + -3y2 + -1y4 + -1y4] + (7y4 + -5y2 + -7) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -3y2 + -2y4] + (7y4 + -5y2 + -7) = 0

Remove brackets around [-2 + -3y2 + -2y4]
-2 + -3y2 + -2y4 + (7y4 + -5y2 + -7) = 0

Reorder the terms:
-2 + -3y2 + -2y4 + (-7 + -5y2 + 7y4) = 0

Remove parenthesis around (-7 + -5y2 + 7y4)
-2 + -3y2 + -2y4 + -7 + -5y2 + 7y4 = 0

Reorder the terms:
-2 + -7 + -3y2 + -5y2 + -2y4 + 7y4 = 0

Combine like terms: -2 + -7 = -9
-9 + -3y2 + -5y2 + -2y4 + 7y4 = 0

Combine like terms: -3y2 + -5y2 = -8y2
-9 + -8y2 + -2y4 + 7y4 = 0

Combine like terms: -2y4 + 7y4 = 5y4
-9 + -8y2 + 5y4 = 0

Solving
-9 + -8y2 + 5y4 = 0

Solving for variable 'y'.

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

Divide each side by '5'.
-1.8 + -1.6y2 + y4 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -1.6y2 + 1.8 + y4 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -1.6y2 + y4 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -1.6y2 + y4 = 0 + 1.8
-1.6y2 + y4 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-1.6y2 + y4 = 1.8

The y term is -1.6y2.  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.
-1.6y2 + 0.64 + y4 = 1.8 + 0.64

Reorder the terms:
0.64 + -1.6y2 + y4 = 1.8 + 0.64

Combine like terms: 1.8 + 0.64 = 2.44
0.64 + -1.6y2 + y4 = 2.44

Factor a perfect square on the left side:
(y2 + -0.8)(y2 + -0.8) = 2.44

Calculate the square root of the right side: 1.562049935

Break this problem into two subproblems by setting 
(y2 + -0.8) equal to 1.562049935 and -1.562049935.


Subproblem 1
y2 + -0.8 = 1.562049935

Simplifying
y2 + -0.8 = 1.562049935

Reorder the terms:
-0.8 + y2 = 1.562049935

Solving
-0.8 + y2 = 1.562049935

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 + y2 = 1.562049935 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + y2 = 1.562049935 + 0.8
y2 = 1.562049935 + 0.8

Combine like terms: 1.562049935 + 0.8 = 2.362049935
y2 = 2.362049935

Simplifying
y2 = 2.362049935

Take the square root of each side:
y = {-1.536896202, 1.536896202}


Subproblem 2
y2 + -0.8 = -1.562049935

Simplifying
y2 + -0.8 = -1.562049935

Reorder the terms:
-0.8 + y2 = -1.562049935

Solving
-0.8 + y2 = -1.562049935

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 + y2 = -1.562049935 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + y2 = -1.562049935 + 0.8
y2 = -1.562049935 + 0.8

Combine like terms: -1.562049935 + 0.8 = -0.762049935
y2 = -0.762049935

Simplifying
y2 = -0.762049935

Reorder the terms:
0.762049935 + y2 = -0.762049935 + 0.762049935

Combine like terms: -0.762049935 + 0.762049935 = 0.000000000
0.762049935 + 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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