-27=x^4-12x^2

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Solution for -27=x^4-12x^2 equation: 


Simplifying
-27 = x4 + -12x2

Reorder the terms:
-27 = -12x2 + x4

Solving
-27 = -12x2 + x4

Solving for variable 'x'.

Reorder the terms:
-27 + 12x2 + -1x4 = -12x2 + 12x2 + x4 + -1x4

Combine like terms: -12x2 + 12x2 = 0
-27 + 12x2 + -1x4 = 0 + x4 + -1x4
-27 + 12x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-27 + 12x2 + -1x4 = 0

Factor a trinomial.
(-9 + x2)(3 + -1x2) = 0

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


Subproblem 1
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}

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 = {-1.732050808, 1.732050808, -3, 3}

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