-x^4+21x^2+100=180

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Solution for -x^4+21x^2+100=180 equation: 


Simplifying
-1x4 + 21x2 + 100 = 180

Reorder the terms:
100 + 21x2 + -1x4 = 180

Solving
100 + 21x2 + -1x4 = 180

Solving for variable 'x'.

Reorder the terms:
100 + -180 + 21x2 + -1x4 = 180 + -180

Combine like terms: 100 + -180 = -80
-80 + 21x2 + -1x4 = 180 + -180

Combine like terms: 180 + -180 = 0
-80 + 21x2 + -1x4 = 0

Factor a trinomial.
(-16 + x2)(5 + -1x2) = 0

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


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

Simplifying
5 + -1x2 = 0

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

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

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

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 3
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {-2.236067978, 2.236067978, -4, 4}

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