20x^4-6x^2-14=0

Solution for 20x^4-6x^2-14=0 equation:

Simplifying
20x4 + -6x2 + -14 = 0

Reorder the terms:
-14 + -6x2 + 20x4 = 0

Solving
-14 + -6x2 + 20x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -3x2 + 10x4) = 0

Factor a trinomial.
2((-7 + -10x2)(1 + -1x2)) = 0

Factor a difference between two squares.
2((-7 + -10x2)((1 + x)(1 + -1x))) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -10x2)' equal to zero and attempt to solve:

Simplifying
-7 + -10x2 = 0

Solving
-7 + -10x2 = 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 + -10x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10x2 = 0 + 7
-10x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-10x2 = 7

Divide each side by '-10'.
x2 = -0.7

Simplifying
x2 = -0.7

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 '(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 3
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}