F(x^2)=2x^6-x^2

Solution for F(x^2)=2x^6-x^2 equation:

Simplifying
F(x2) = 2x6 + -1x2

Multiply F * x2
x2F = 2x6 + -1x2

Reorder the terms:
x2F = -1x2 + 2x6

Solving
x2F = -1x2 + 2x6

Solving for variable 'x'.

Reorder the terms:
x2 + x2F + -2x6 = -1x2 + 2x6 + x2 + -2x6

Reorder the terms:
x2 + x2F + -2x6 = -1x2 + x2 + 2x6 + -2x6

Combine like terms: -1x2 + x2 = 0
x2 + x2F + -2x6 = 0 + 2x6 + -2x6
x2 + x2F + -2x6 = 2x6 + -2x6

Combine like terms: 2x6 + -2x6 = 0
x2 + x2F + -2x6 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + F + -2x4) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + F + -2x4)' equal to zero and attempt to solve:

Simplifying
1 + F + -2x4 = 0

Solving
1 + F + -2x4 = 0

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

Add '-1' to each side of the equation.
1 + F + -1 + -2x4 = 0 + -1

Reorder the terms:
1 + -1 + F + -2x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + F + -2x4 = 0 + -1
F + -2x4 = 0 + -1

Combine like terms: 0 + -1 = -1
F + -2x4 = -1

Add '-1F' to each side of the equation.
F + -1F + -2x4 = -1 + -1F

Combine like terms: F + -1F = 0
0 + -2x4 = -1 + -1F
-2x4 = -1 + -1F

Divide each side by '-2'.
x4 = 0.5 + 0.5F

Simplifying
x4 = 0.5 + 0.5F

The solution to this equation could not be determined.

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