x^4+3x^2+1=1

Solution for x^4+3x^2+1=1 equation:

Simplifying
x4 + 3x2 + 1 = 1

Reorder the terms:
1 + 3x2 + x4 = 1

Add '-1' to each side of the equation.
1 + 3x2 + -1 + x4 = 1 + -1

Reorder the terms:
1 + -1 + 3x2 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + 3x2 + x4 = 1 + -1
3x2 + x4 = 1 + -1

Combine like terms: 1 + -1 = 0
3x2 + x4 = 0

Solving
3x2 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(3 + x2) = 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 '(3 + x2)' equal to zero and attempt to solve:

Simplifying
3 + x2 = 0

Solving
3 + x2 = 0

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

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

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

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

Simplifying
x2 = -3

The solution to this equation could not be determined.

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