[-(y^4-y^2+1)-(y^4+6y^2+1)]+(7y^4-9y^2-4)=

Solution for [-(y^4-y^2+1)-(y^4+6y^2+1)]+(7y^4-9y^2-4)= equation:

Simplifying
[-1(y4 + -1y2 + 1) + -1(y4 + 6y2 + 1)] + (7y4 + -9y2 + -4) = 0

Reorder the terms:
[-1(1 + -1y2 + y4) + -1(y4 + 6y2 + 1)] + (7y4 + -9y2 + -4) = 0
[(1 * -1 + -1y2 * -1 + y4 * -1) + -1(y4 + 6y2 + 1)] + (7y4 + -9y2 + -4) = 0
[(-1 + 1y2 + -1y4) + -1(y4 + 6y2 + 1)] + (7y4 + -9y2 + -4) = 0

Reorder the terms:
[-1 + 1y2 + -1y4 + -1(1 + 6y2 + y4)] + (7y4 + -9y2 + -4) = 0
[-1 + 1y2 + -1y4 + (1 * -1 + 6y2 * -1 + y4 * -1)] + (7y4 + -9y2 + -4) = 0
[-1 + 1y2 + -1y4 + (-1 + -6y2 + -1y4)] + (7y4 + -9y2 + -4) = 0

Reorder the terms:
[-1 + -1 + 1y2 + -6y2 + -1y4 + -1y4] + (7y4 + -9y2 + -4) = 0

Combine like terms: -1 + -1 = -2
[-2 + 1y2 + -6y2 + -1y4 + -1y4] + (7y4 + -9y2 + -4) = 0

Combine like terms: 1y2 + -6y2 = -5y2
[-2 + -5y2 + -1y4 + -1y4] + (7y4 + -9y2 + -4) = 0

Combine like terms: -1y4 + -1y4 = -2y4
[-2 + -5y2 + -2y4] + (7y4 + -9y2 + -4) = 0

Remove brackets around [-2 + -5y2 + -2y4]
-2 + -5y2 + -2y4 + (7y4 + -9y2 + -4) = 0

Reorder the terms:
-2 + -5y2 + -2y4 + (-4 + -9y2 + 7y4) = 0

Remove parenthesis around (-4 + -9y2 + 7y4)
-2 + -5y2 + -2y4 + -4 + -9y2 + 7y4 = 0

Reorder the terms:
-2 + -4 + -5y2 + -9y2 + -2y4 + 7y4 = 0

Combine like terms: -2 + -4 = -6
-6 + -5y2 + -9y2 + -2y4 + 7y4 = 0

Combine like terms: -5y2 + -9y2 = -14y2
-6 + -14y2 + -2y4 + 7y4 = 0

Combine like terms: -2y4 + 7y4 = 5y4
-6 + -14y2 + 5y4 = 0

Solving
-6 + -14y2 + 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'.
-1.2 + -2.8y2 + y4 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -2.8y2 + 1.2 + y4 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -2.8y2 + y4 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -2.8y2 + y4 = 0 + 1.2
-2.8y2 + y4 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-2.8y2 + y4 = 1.2

The y term is -2.8y2.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8y2 + 1.96 + y4 = 1.2 + 1.96

Reorder the terms:
1.96 + -2.8y2 + y4 = 1.2 + 1.96

Combine like terms: 1.2 + 1.96 = 3.16
1.96 + -2.8y2 + y4 = 3.16

Factor a perfect square on the left side:
(y2 + -1.4)(y2 + -1.4) = 3.16

Calculate the square root of the right side: 1.777638883

Break this problem into two subproblems by setting 
(y2 + -1.4) equal to 1.777638883 and -1.777638883.

Subproblem 1
y2 + -1.4 = 1.777638883

Simplifying
y2 + -1.4 = 1.777638883

Reorder the terms:
-1.4 + y2 = 1.777638883

Solving
-1.4 + y2 = 1.777638883

Solving for variable 'y'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + y2 = 1.777638883 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + y2 = 1.777638883 + 1.4
y2 = 1.777638883 + 1.4

Combine like terms: 1.777638883 + 1.4 = 3.177638883
y2 = 3.177638883

Simplifying
y2 = 3.177638883

Take the square root of each side:
y = {-1.782593303, 1.782593303}

Subproblem 2
y2 + -1.4 = -1.777638883

Simplifying
y2 + -1.4 = -1.777638883

Reorder the terms:
-1.4 + y2 = -1.777638883

Solving
-1.4 + y2 = -1.777638883

Solving for variable 'y'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + y2 = -1.777638883 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + y2 = -1.777638883 + 1.4
y2 = -1.777638883 + 1.4

Combine like terms: -1.777638883 + 1.4 = -0.377638883
y2 = -0.377638883

Simplifying
y2 = -0.377638883

Reorder the terms:
0.377638883 + y2 = -0.377638883 + 0.377638883

Combine like terms: -0.377638883 + 0.377638883 = 0.000000000
0.377638883 + 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.