a^4-12a^2+27=0

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Solution for a^4-12a^2+27=0 equation: 


Simplifying
a4 + -12a2 + 27 = 0

Reorder the terms:
27 + -12a2 + a4 = 0

Solving
27 + -12a2 + a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(3 + -1a2)(9 + -1a2) = 0

Factor a difference between two squares.
(3 + -1a2)((3 + a)(3 + -1a)) = 0


Subproblem 1
Set the factor '(3 + -1a2)' equal to zero and attempt to solve:

Simplifying
3 + -1a2 = 0

Solving
3 + -1a2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a2 = 0 + -3
-1a2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1a2 = -3

Divide each side by '-1'.
a2 = 3

Simplifying
a2 = 3

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

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

Simplifying
3 + a = 0

Solving
3 + a = 0

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

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

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

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

Simplifying
a = -3

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

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

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

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

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

Simplifying
a = 3
Solution
a = {-1.732050808, 1.732050808, -3, 3}

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