0=-18x^4-96x^2+384

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Solution for 0=-18x^4-96x^2+384 equation: 


Simplifying
0 = -18x4 + -96x2 + 384

Reorder the terms:
0 = 384 + -96x2 + -18x4

Solving
0 = 384 + -96x2 + -18x4

Solving for variable 'x'.

Combine like terms: 0 + -384 = -384
-384 + 96x2 + 18x4 = 384 + -96x2 + -18x4 + -384 + 96x2 + 18x4

Reorder the terms:
-384 + 96x2 + 18x4 = 384 + -384 + -96x2 + 96x2 + -18x4 + 18x4

Combine like terms: 384 + -384 = 0
-384 + 96x2 + 18x4 = 0 + -96x2 + 96x2 + -18x4 + 18x4
-384 + 96x2 + 18x4 = -96x2 + 96x2 + -18x4 + 18x4

Combine like terms: -96x2 + 96x2 = 0
-384 + 96x2 + 18x4 = 0 + -18x4 + 18x4
-384 + 96x2 + 18x4 = -18x4 + 18x4

Combine like terms: -18x4 + 18x4 = 0
-384 + 96x2 + 18x4 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-64 + 16x2 + 3x4) = 0

Factor a trinomial.
6((-8 + -1x2)(8 + -3x2)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-8 + -1x2)' equal to zero and attempt to solve:

Simplifying
-8 + -1x2 = 0

Solving
-8 + -1x2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x2 = 0 + 8
-1x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1x2 = 8

Divide each side by '-1'.
x2 = -8

Simplifying
x2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(8 + -3x2)' equal to zero and attempt to solve:

Simplifying
8 + -3x2 = 0

Solving
8 + -3x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x2 = 0 + -8
-3x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3x2 = -8

Divide each side by '-3'.
x2 = 2.666666667

Simplifying
x2 = 2.666666667

Take the square root of each side:
x = {-1.632993162, 1.632993162}
Solution
x = {-1.632993162, 1.632993162}

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