[-(y^4-y^2+1)-(y^4+2y^2+1)]+(5y^4-6y^2-8)=0

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Solution for [-(y^4-y^2+1)-(y^4+2y^2+1)]+(5y^4-6y^2-8)=0 equation: 


Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 2y2 + 1)] + (5y4 + -6y2 + -8) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 2y2 + 1)] + (5y4 + -6y2 + -8) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 2y2 + 1)] + (5y4 + -6y2 + -8) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 2y2 + 1)] + (5y4 + -6y2 + -8) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 2y2 + y4)] + (5y4 + -6y2 + -8) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 2y2 * -1 + y4 * -1)] + (5y4 + -6y2 + -8) = 0
[-1 + 1y2 + -1y4 + (-1 + -2y2 + -1y4)] + (5y4 + -6y2 + -8) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -2y2 + -1y4 + -1y4] + (5y4 + -6y2 + -8) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -2y2 + -1y4 + -1y4] + (5y4 + -6y2 + -8) = 0

Combine like terms: 1y2 + -2y2 = -1y2
[-2 + -1y2 + -1y4 + -1y4] + (5y4 + -6y2 + -8) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -1y2 + -2y4] + (5y4 + -6y2 + -8) = 0

Remove brackets around [-2 + -1y2 + -2y4]
-2 + -1y2 + -2y4 + (5y4 + -6y2 + -8) = 0

Reorder the terms:
-2 + -1y2 + -2y4 + (-8 + -6y2 + 5y4) = 0

Remove parenthesis around (-8 + -6y2 + 5y4)
-2 + -1y2 + -2y4 + -8 + -6y2 + 5y4 = 0

Reorder the terms:
-2 + -8 + -1y2 + -6y2 + -2y4 + 5y4 = 0

Combine like terms: -2 + -8 = -10
-10 + -1y2 + -6y2 + -2y4 + 5y4 = 0

Combine like terms: -1y2 + -6y2 = -7y2
-10 + -7y2 + -2y4 + 5y4 = 0

Combine like terms: -2y4 + 5y4 = 3y4
-10 + -7y2 + 3y4 = 0

Solving
-10 + -7y2 + 3y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y2)(10 + -3y2) = 0


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

Simplifying
-1 + -1y2 = 0

Solving
-1 + -1y2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1y2 = 0 + 1
-1y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1y2 = 1

Divide each side by '-1'.
y2 = -1

Simplifying
y2 = -1

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(10 + -3y2)' equal to zero and attempt to solve:

Simplifying
10 + -3y2 = 0

Solving
10 + -3y2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3y2 = 0 + -10
-3y2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3y2 = -10

Divide each side by '-3'.
y2 = 3.333333333

Simplifying
y2 = 3.333333333

Take the square root of each side:
y = {-1.825741858, 1.825741858}
Solution
y = {-1.825741858, 1.825741858}

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