a^4+32=12a^2

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Solution for a^4+32=12a^2 equation: 


Simplifying
a4 + 32 = 12a2

Reorder the terms:
32 + a4 = 12a2

Solving
32 + a4 = 12a2

Solving for variable 'a'.

Reorder the terms:
32 + -12a2 + a4 = 12a2 + -12a2

Combine like terms: 12a2 + -12a2 = 0
32 + -12a2 + a4 = 0

Factor a trinomial.
(4 + -1a2)(8 + -1a2) = 0

Factor a difference between two squares.
((2 + a)(2 + -1a))(8 + -1a2) = 0


Subproblem 1
Set the factor '(8 + -1a2)' equal to zero and attempt to solve:

Simplifying
8 + -1a2 = 0

Solving
8 + -1a2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a2 = 0 + -8
-1a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1a2 = -8

Divide each side by '-1'.
a2 = 8

Simplifying
a2 = 8

Take the square root of each side:
a = {-2.828427125, 2.828427125}

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

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2

Subproblem 3
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

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

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

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

Simplifying
a = 2
Solution
a = {-2.828427125, 2.828427125, -2, 2}

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