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

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


Simplifying
0 = 4x4 + -5x2 + 1

Reorder the terms:
0 = 1 + -5x2 + 4x4

Solving
0 = 1 + -5x2 + 4x4

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 5x2 + -4x4 = 1 + -5x2 + 4x4 + -1 + 5x2 + -4x4

Reorder the terms:
-1 + 5x2 + -4x4 = 1 + -1 + -5x2 + 5x2 + 4x4 + -4x4

Combine like terms: 1 + -1 = 0
-1 + 5x2 + -4x4 = 0 + -5x2 + 5x2 + 4x4 + -4x4
-1 + 5x2 + -4x4 = -5x2 + 5x2 + 4x4 + -4x4

Combine like terms: -5x2 + 5x2 = 0
-1 + 5x2 + -4x4 = 0 + 4x4 + -4x4
-1 + 5x2 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
-1 + 5x2 + -4x4 = 0

Factor a trinomial.
(-1 + x2)(1 + -4x2) = 0

Factor a difference between two squares.
((1 + x)(-1 + x))(1 + -4x2) = 0

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


Subproblem 1
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 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 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 4
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1, 1, -0.5, 0.5}

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