4x^2+x^4-21=0

Solution for 4x^2+x^4-21=0 equation:

Simplifying
4x2 + x4 + -21 = 0

Reorder the terms:
-21 + 4x2 + x4 = 0

Solving
-21 + 4x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(-7 + -1x2)' equal to zero and attempt to solve:

Simplifying
-7 + -1x2 = 0

Solving
-7 + -1x2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x2 = 0 + 7
-1x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1x2 = 7

Divide each side by '-1'.
x2 = -7

Simplifying
x2 = -7

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

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

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

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-1.732050808, 1.732050808}