0=5x^4-6x^2+1

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Solution for 0=5x^4-6x^2+1 equation: 


Simplifying
0 = 5x4 + -6x2 + 1

Reorder the terms:
0 = 1 + -6x2 + 5x4

Solving
0 = 1 + -6x2 + 5x4

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 6x2 + -5x4 = 1 + -6x2 + 5x4 + -1 + 6x2 + -5x4

Reorder the terms:
-1 + 6x2 + -5x4 = 1 + -1 + -6x2 + 6x2 + 5x4 + -5x4

Combine like terms: 1 + -1 = 0
-1 + 6x2 + -5x4 = 0 + -6x2 + 6x2 + 5x4 + -5x4
-1 + 6x2 + -5x4 = -6x2 + 6x2 + 5x4 + -5x4

Combine like terms: -6x2 + 6x2 = 0
-1 + 6x2 + -5x4 = 0 + 5x4 + -5x4
-1 + 6x2 + -5x4 = 5x4 + -5x4

Combine like terms: 5x4 + -5x4 = 0
-1 + 6x2 + -5x4 = 0

Factor a trinomial.
(-1 + x2)(1 + -5x2) = 0

Factor a difference between two squares.
((1 + x)(-1 + x))(1 + -5x2) = 0


Subproblem 1
Set the factor '(1 + -5x2)' equal to zero and attempt to solve:

Simplifying
1 + -5x2 = 0

Solving
1 + -5x2 = 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 + -5x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x2 = 0 + -1
-5x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-5x2 = -1

Divide each side by '-5'.
x2 = 0.2

Simplifying
x2 = 0.2

Take the square root of each side:
x = {-0.447213596, 0.447213596}

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 + 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
Solution
x = {-0.447213596, 0.447213596, -1, 1}

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