(-2b^6+3b^4-b^2)-(b^6+2b^4+2b^2)=

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Solution for (-2b^6+3b^4-b^2)-(b^6+2b^4+2b^2)= equation: 


Simplifying
(-2b6 + 3b4 + -1b2) + -1(b6 + 2b4 + 2b2) = 0

Reorder the terms:
(-1b2 + 3b4 + -2b6) + -1(b6 + 2b4 + 2b2) = 0

Remove parenthesis around (-1b2 + 3b4 + -2b6)
-1b2 + 3b4 + -2b6 + -1(b6 + 2b4 + 2b2) = 0

Reorder the terms:
-1b2 + 3b4 + -2b6 + -1(2b2 + 2b4 + b6) = 0
-1b2 + 3b4 + -2b6 + (2b2 * -1 + 2b4 * -1 + b6 * -1) = 0
-1b2 + 3b4 + -2b6 + (-2b2 + -2b4 + -1b6) = 0

Reorder the terms:
-1b2 + -2b2 + 3b4 + -2b4 + -2b6 + -1b6 = 0

Combine like terms: -1b2 + -2b2 = -3b2
-3b2 + 3b4 + -2b4 + -2b6 + -1b6 = 0

Combine like terms: 3b4 + -2b4 = 1b4
-3b2 + 1b4 + -2b6 + -1b6 = 0

Combine like terms: -2b6 + -1b6 = -3b6
-3b2 + 1b4 + -3b6 = 0

Solving
-3b2 + 1b4 + -3b6 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), 'b2'.
b2(-3 + b2 + -3b4) = 0


Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve:

Simplifying
b2 = 0

Solving
b2 = 0

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

Simplifying
b2 = 0

Take the square root of each side:
b = {0}

Subproblem 2
Set the factor '(-3 + b2 + -3b4)' equal to zero and attempt to solve:

Simplifying
-3 + b2 + -3b4 = 0

Solving
-3 + b2 + -3b4 = 0

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

Divide each side by '-3'.
1 + -0.3333333333b2 + b4 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.3333333333b2 + -1 + b4 = 0 + -1

Reorder the terms:
1 + -1 + -0.3333333333b2 + b4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.3333333333b2 + b4 = 0 + -1
-0.3333333333b2 + b4 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.3333333333b2 + b4 = -1

The b term is b2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333b2 + 0.25 + b4 = -1 + 0.25

Reorder the terms:
0.25 + -0.3333333333b2 + b4 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -0.3333333333b2 + b4 = -0.75

Factor a perfect square on the left side:
(b2 + 0.5)(b2 + 0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}

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