4x^6+8x^4+7x^2+2=2

Solution for 4x^6+8x^4+7x^2+2=2 equation:

Simplifying
4x6 + 8x4 + 7x2 + 2 = 2

Reorder the terms:
2 + 7x2 + 8x4 + 4x6 = 2

Add '-2' to each side of the equation.
2 + 7x2 + 8x4 + -2 + 4x6 = 2 + -2

Reorder the terms:
2 + -2 + 7x2 + 8x4 + 4x6 = 2 + -2

Combine like terms: 2 + -2 = 0
0 + 7x2 + 8x4 + 4x6 = 2 + -2
7x2 + 8x4 + 4x6 = 2 + -2

Combine like terms: 2 + -2 = 0
7x2 + 8x4 + 4x6 = 0

Solving
7x2 + 8x4 + 4x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(7 + 8x2 + 4x4) = 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 '(7 + 8x2 + 4x4)' equal to zero and attempt to solve:

Simplifying
7 + 8x2 + 4x4 = 0

Solving
7 + 8x2 + 4x4 = 0

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

Divide each side by '4'.
1.75 + 2x2 + x4 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 2x2 + -1.75 + x4 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 2x2 + x4 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 2x2 + x4 = 0 + -1.75
2x2 + x4 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
2x2 + x4 = -1.75

The x term is 2x2.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x2 + 1 + x4 = -1.75 + 1

Reorder the terms:
1 + 2x2 + x4 = -1.75 + 1

Combine like terms: -1.75 + 1 = -0.75
1 + 2x2 + x4 = -0.75

Factor a perfect square on the left side:
(x2 + 1)(x2 + 1) = -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
x = {0}