54a^4-288a^2+384=

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Solution for 54a^4-288a^2+384= equation: 


Simplifying
54a4 + -288a2 + 384 = 0

Reorder the terms:
384 + -288a2 + 54a4 = 0

Solving
384 + -288a2 + 54a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(64 + -48a2 + 9a4) = 0

Factor a trinomial.
6((8 + -3a2)(8 + -3a2)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(8 + -3a2)' equal to zero and attempt to solve:

Simplifying
8 + -3a2 = 0

Solving
8 + -3a2 = 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 + -3a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a2 = 0 + -8
-3a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3a2 = -8

Divide each side by '-3'.
a2 = 2.666666667

Simplifying
a2 = 2.666666667

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

Subproblem 2
Set the factor '(8 + -3a2)' equal to zero and attempt to solve:

Simplifying
8 + -3a2 = 0

Solving
8 + -3a2 = 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 + -3a2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a2 = 0 + -8
-3a2 = 0 + -8

Combine like terms: 0 + -8 = -8
-3a2 = -8

Divide each side by '-3'.
a2 = 2.666666667

Simplifying
a2 = 2.666666667

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

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