4x^4-21x^2+20=0

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Solution for 4x^4-21x^2+20=0 equation: 


Simplifying
4x4 + -21x2 + 20 = 0

Reorder the terms:
20 + -21x2 + 4x4 = 0

Solving
20 + -21x2 + 4x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -4x2)(4 + -1x2) = 0

Factor a difference between two squares.
(5 + -4x2)((2 + x)(2 + -1x)) = 0


Subproblem 1
Set the factor '(5 + -4x2)' equal to zero and attempt to solve:

Simplifying
5 + -4x2 = 0

Solving
5 + -4x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x2 = 0 + -5

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

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

Divide each side by '-4'.
x2 = 1.25

Simplifying
x2 = 1.25

Take the square root of each side:
x = {-1.118033989, 1.118033989}

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

Simplifying
2 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.118033989, 1.118033989, -2, 2}

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