0=-x^4+18x^2-32

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Solution for 0=-x^4+18x^2-32 equation: 


Simplifying
0 = -1x4 + 18x2 + -32

Reorder the terms:
0 = -32 + 18x2 + -1x4

Solving
0 = -32 + 18x2 + -1x4

Solving for variable 'x'.

Combine like terms: 0 + 32 = 32
32 + -18x2 + x4 = -32 + 18x2 + -1x4 + 32 + -18x2 + x4

Reorder the terms:
32 + -18x2 + x4 = -32 + 32 + 18x2 + -18x2 + -1x4 + x4

Combine like terms: -32 + 32 = 0
32 + -18x2 + x4 = 0 + 18x2 + -18x2 + -1x4 + x4
32 + -18x2 + x4 = 18x2 + -18x2 + -1x4 + x4

Combine like terms: 18x2 + -18x2 = 0
32 + -18x2 + x4 = 0 + -1x4 + x4
32 + -18x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
32 + -18x2 + x4 = 0

Factor a trinomial.
(2 + -1x2)(16 + -1x2) = 0

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


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

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1.414213562, 1.414213562, -4, 4}

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