9X^8-21X^4+12=0

Solution for 9X^8-21X^4+12=0 equation:

Simplifying
9X8 + -21X4 + 12 = 0

Reorder the terms:
12 + -21X4 + 9X8 = 0

Solving
12 + -21X4 + 9X8 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -7X4 + 3X8) = 0

Factor a trinomial.
3((1 + -1X4)(4 + -3X4)) = 0

Factor a difference between two squares.
3(((1 + X2)(1 + -1X2))(4 + -3X4)) = 0

Factor a difference between two squares.
3(((1 + X2)((1 + X)(1 + -1X)))(4 + -3X4)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -3X4)' equal to zero and attempt to solve:

Simplifying
4 + -3X4 = 0

Solving
4 + -3X4 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3X4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3X4 = 0 + -4
-3X4 = 0 + -4

Combine like terms: 0 + -4 = -4
-3X4 = -4

Divide each side by '-3'.
X4 = 1.333333333

Simplifying
X4 = 1.333333333

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 '(1 + X2)' equal to zero and attempt to solve:

Simplifying
1 + X2 = 0

Solving
1 + X2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + X2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + X2 = 0 + -1
X2 = 0 + -1

Combine like terms: 0 + -1 = -1
X2 = -1

Simplifying
X2 = -1

The solution to this equation could not be determined.

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

Simplifying
1 + X = 0

Solving
1 + X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + X = 0 + -1
X = 0 + -1

Combine like terms: 0 + -1 = -1
X = -1

Simplifying
X = -1
Subproblem 4
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1X = 0 + -1
-1X = 0 + -1

Combine like terms: 0 + -1 = -1
-1X = -1

Divide each side by '-1'.
X = 1

Simplifying
X = 1
Solution
X = {-1, 1}