0=3x^4-14x^2+8

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Solution for 0=3x^4-14x^2+8 equation: 


Simplifying
0 = 3x4 + -14x2 + 8

Reorder the terms:
0 = 8 + -14x2 + 3x4

Solving
0 = 8 + -14x2 + 3x4

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + 14x2 + -3x4 = 8 + -14x2 + 3x4 + -8 + 14x2 + -3x4

Reorder the terms:
-8 + 14x2 + -3x4 = 8 + -8 + -14x2 + 14x2 + 3x4 + -3x4

Combine like terms: 8 + -8 = 0
-8 + 14x2 + -3x4 = 0 + -14x2 + 14x2 + 3x4 + -3x4
-8 + 14x2 + -3x4 = -14x2 + 14x2 + 3x4 + -3x4

Combine like terms: -14x2 + 14x2 = 0
-8 + 14x2 + -3x4 = 0 + 3x4 + -3x4
-8 + 14x2 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
-8 + 14x2 + -3x4 = 0

Factor a trinomial.
(-4 + x2)(2 + -3x2) = 0

Factor a difference between two squares.
((2 + x)(-2 + x))(2 + -3x2) = 0


Subproblem 1
Set the factor '(2 + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + -3x2 = 0

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

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

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

Divide each side by '-3'.
x2 = 0.6666666667

Simplifying
x2 = 0.6666666667

Take the square root of each side:
x = {-0.816496581, 0.816496581}

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2
Solution
x = {-0.816496581, 0.816496581, -2, 2}

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