2x^2(x^4+3x^2-5)=

Solution for 2x^2(x^4+3x^2-5)= equation:

Simplifying
2x2(x4 + 3x2 + -5) = 0

Reorder the terms:
2x2(-5 + 3x2 + x4) = 0
(-5 * 2x2 + 3x2 * 2x2 + x4 * 2x2) = 0
(-10x2 + 6x4 + 2x6) = 0

Solving
-10x2 + 6x4 + 2x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-5 + 3x2 + x4) = 0

Ignore the factor 2.
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 '(-5 + 3x2 + x4)' equal to zero and attempt to solve:

Simplifying
-5 + 3x2 + x4 = 0

Solving
-5 + 3x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3x2 + 5 + x4 = 0 + 5

Reorder the terms:
-5 + 5 + 3x2 + x4 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x2 + x4 = 0 + 5
3x2 + x4 = 0 + 5

Combine like terms: 0 + 5 = 5
3x2 + x4 = 5

The x term is 3x2.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x2 + 2.25 + x4 = 5 + 2.25

Reorder the terms:
2.25 + 3x2 + x4 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + 3x2 + x4 = 7.25

Factor a perfect square on the left side:
(x2 + 1.5)(x2 + 1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x2 + 1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
x2 + 1.5 = 2.692582404

Simplifying
x2 + 1.5 = 2.692582404

Reorder the terms:
1.5 + x2 = 2.692582404

Solving
1.5 + x2 = 2.692582404

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x2 = 2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x2 = 2.692582404 + -1.5
x2 = 2.692582404 + -1.5

Combine like terms: 2.692582404 + -1.5 = 1.192582404
x2 = 1.192582404

Simplifying
x2 = 1.192582404

Take the square root of each side:
x = {-1.092054213, 1.092054213}

Subproblem 2
x2 + 1.5 = -2.692582404

Simplifying
x2 + 1.5 = -2.692582404

Reorder the terms:
1.5 + x2 = -2.692582404

Solving
1.5 + x2 = -2.692582404

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x2 = -2.692582404 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x2 = -2.692582404 + -1.5
x2 = -2.692582404 + -1.5

Combine like terms: -2.692582404 + -1.5 = -4.192582404
x2 = -4.192582404

Simplifying
x2 = -4.192582404

Reorder the terms:
4.192582404 + x2 = -4.192582404 + 4.192582404

Combine like terms: -4.192582404 + 4.192582404 = 0.000000000
4.192582404 + x2 = 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.
Solution
x = {0}