[-(y^4-y^2+1)-(y^4+6y^2+1)]+(8y^4-7y^2-12)=

Solution for [-(y^4-y^2+1)-(y^4+6y^2+1)]+(8y^4-7y^2-12)= equation:

Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 6y2 + 1)] + (8y4 + -7y2 + -12) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 6y2 + 1)] + (8y4 + -7y2 + -12) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 6y2 + 1)] + (8y4 + -7y2 + -12) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 6y2 + 1)] + (8y4 + -7y2 + -12) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 6y2 + y4)] + (8y4 + -7y2 + -12) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 6y2 * -1 + y4 * -1)] + (8y4 + -7y2 + -12) = 0
[-1 + 1y2 + -1y4 + (-1 + -6y2 + -1y4)] + (8y4 + -7y2 + -12) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -6y2 + -1y4 + -1y4] + (8y4 + -7y2 + -12) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -6y2 + -1y4 + -1y4] + (8y4 + -7y2 + -12) = 0

Combine like terms: 1y2 + -6y2 = -5y2
[-2 + -5y2 + -1y4 + -1y4] + (8y4 + -7y2 + -12) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -5y2 + -2y4] + (8y4 + -7y2 + -12) = 0

Remove brackets around [-2 + -5y2 + -2y4]
-2 + -5y2 + -2y4 + (8y4 + -7y2 + -12) = 0

Reorder the terms:
-2 + -5y2 + -2y4 + (-12 + -7y2 + 8y4) = 0

Remove parenthesis around (-12 + -7y2 + 8y4)
-2 + -5y2 + -2y4 + -12 + -7y2 + 8y4 = 0

Reorder the terms:
-2 + -12 + -5y2 + -7y2 + -2y4 + 8y4 = 0

Combine like terms: -2 + -12 = -14
-14 + -5y2 + -7y2 + -2y4 + 8y4 = 0

Combine like terms: -5y2 + -7y2 = -12y2
-14 + -12y2 + -2y4 + 8y4 = 0

Combine like terms: -2y4 + 8y4 = 6y4
-14 + -12y2 + 6y4 = 0

Solving
-14 + -12y2 + 6y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -6y2 + 3y4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -6y2 + 3y4)' equal to zero and attempt to solve:

Simplifying
-7 + -6y2 + 3y4 = 0

Solving
-7 + -6y2 + 3y4 = 0

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

Divide each side by '3'.
-2.333333333 + -2y2 + y4 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -2y2 + 2.333333333 + y4 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -2y2 + y4 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -2y2 + y4 = 0 + 2.333333333
-2y2 + y4 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-2y2 + y4 = 2.333333333

The y term is -2y2.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y2 + 1 + y4 = 2.333333333 + 1

Reorder the terms:
1 + -2y2 + y4 = 2.333333333 + 1

Combine like terms: 2.333333333 + 1 = 3.333333333
1 + -2y2 + y4 = 3.333333333

Factor a perfect square on the left side:
(y2 + -1)(y2 + -1) = 3.333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(y2 + -1) equal to 1.825741858 and -1.825741858.

Subproblem 1
y2 + -1 = 1.825741858

Simplifying
y2 + -1 = 1.825741858

Reorder the terms:
-1 + y2 = 1.825741858

Solving
-1 + y2 = 1.825741858

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y2 = 1.825741858 + 1

Combine like terms: -1 + 1 = 0
0 + y2 = 1.825741858 + 1
y2 = 1.825741858 + 1

Combine like terms: 1.825741858 + 1 = 2.825741858
y2 = 2.825741858

Simplifying
y2 = 2.825741858

Take the square root of each side:
y = {-1.680994306, 1.680994306}

Subproblem 2
y2 + -1 = -1.825741858

Simplifying
y2 + -1 = -1.825741858

Reorder the terms:
-1 + y2 = -1.825741858

Solving
-1 + y2 = -1.825741858

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y2 = -1.825741858 + 1

Combine like terms: -1 + 1 = 0
0 + y2 = -1.825741858 + 1
y2 = -1.825741858 + 1

Combine like terms: -1.825741858 + 1 = -0.825741858
y2 = -0.825741858

Simplifying
y2 = -0.825741858

Reorder the terms:
0.825741858 + y2 = -0.825741858 + 0.825741858

Combine like terms: -0.825741858 + 0.825741858 = 0.000000000
0.825741858 + 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.