0=4x^4-14x^2+12

Solution for 0=4x^4-14x^2+12 equation:

Simplifying
0 = 4x4 + -14x2 + 12

Reorder the terms:
0 = 12 + -14x2 + 4x4

Solving
0 = 12 + -14x2 + 4x4

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + 14x2 + -4x4 = 12 + -14x2 + 4x4 + -12 + 14x2 + -4x4

Reorder the terms:
-12 + 14x2 + -4x4 = 12 + -12 + -14x2 + 14x2 + 4x4 + -4x4

Combine like terms: 12 + -12 = 0
-12 + 14x2 + -4x4 = 0 + -14x2 + 14x2 + 4x4 + -4x4
-12 + 14x2 + -4x4 = -14x2 + 14x2 + 4x4 + -4x4

Combine like terms: -14x2 + 14x2 = 0
-12 + 14x2 + -4x4 = 0 + 4x4 + -4x4
-12 + 14x2 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
-12 + 14x2 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7x2 + -2x4) = 0

Factor a trinomial.
2((-2 + x2)(3 + -2x2)) = 0

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

Simplifying
-2 + x2 = 0

Solving
-2 + x2 = 0

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

Add '2' to each side of the equation.
-2 + 2 + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x2 = 0 + 2
x2 = 0 + 2

Combine like terms: 0 + 2 = 2
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(3 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 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 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1.414213562, 1.414213562, -1.224744871, 1.224744871}