0=x^4-15x^2+54

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Solution for 0=x^4-15x^2+54 equation: 


Simplifying
0 = x4 + -15x2 + 54

Reorder the terms:
0 = 54 + -15x2 + x4

Solving
0 = 54 + -15x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -54 = -54
-54 + 15x2 + -1x4 = 54 + -15x2 + x4 + -54 + 15x2 + -1x4

Reorder the terms:
-54 + 15x2 + -1x4 = 54 + -54 + -15x2 + 15x2 + x4 + -1x4

Combine like terms: 54 + -54 = 0
-54 + 15x2 + -1x4 = 0 + -15x2 + 15x2 + x4 + -1x4
-54 + 15x2 + -1x4 = -15x2 + 15x2 + x4 + -1x4

Combine like terms: -15x2 + 15x2 = 0
-54 + 15x2 + -1x4 = 0 + x4 + -1x4
-54 + 15x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-54 + 15x2 + -1x4 = 0

Factor a trinomial.
(-9 + x2)(6 + -1x2) = 0

Factor a difference between two squares.
((3 + x)(-3 + x))(6 + -1x2) = 0


Subproblem 1
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

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

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Solution
x = {-2.449489743, 2.449489743, -3, 3}

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