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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-6 + -6y2 + 2y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -3y2 + y4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -3y2 + y4)' equal to zero and attempt to solve:

Simplifying
-3 + -3y2 + y4 = 0

Solving
-3 + -3y2 + y4 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -3y2 + 3 + y4 = 0 + 3

Reorder the terms:
-3 + 3 + -3y2 + y4 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -3y2 + y4 = 0 + 3
-3y2 + y4 = 0 + 3

Combine like terms: 0 + 3 = 3
-3y2 + y4 = 3

The y term is -3y2.  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.
-3y2 + 2.25 + y4 = 3 + 2.25

Reorder the terms:
2.25 + -3y2 + y4 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + -3y2 + y4 = 5.25

Factor a perfect square on the left side:
(y2 + -1.5)(y2 + -1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(y2 + -1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
y2 + -1.5 = 2.291287847

Simplifying
y2 + -1.5 = 2.291287847

Reorder the terms:
-1.5 + y2 = 2.291287847

Solving
-1.5 + y2 = 2.291287847

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 + y2 = 2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y2 = 2.291287847 + 1.5
y2 = 2.291287847 + 1.5

Combine like terms: 2.291287847 + 1.5 = 3.791287847
y2 = 3.791287847

Simplifying
y2 = 3.791287847

Take the square root of each side:
y = {-1.947122967, 1.947122967}

Subproblem 2
y2 + -1.5 = -2.291287847

Simplifying
y2 + -1.5 = -2.291287847

Reorder the terms:
-1.5 + y2 = -2.291287847

Solving
-1.5 + y2 = -2.291287847

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 + y2 = -2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y2 = -2.291287847 + 1.5
y2 = -2.291287847 + 1.5

Combine like terms: -2.291287847 + 1.5 = -0.791287847
y2 = -0.791287847

Simplifying
y2 = -0.791287847

Reorder the terms:
0.791287847 + y2 = -0.791287847 + 0.791287847

Combine like terms: -0.791287847 + 0.791287847 = 0.000000000
0.791287847 + 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.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.