18a^4-32a^2q^4=

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Solution for 18a^4-32a^2q^4= equation: 


Simplifying
18a4 + -32a2q4 = 0

Reorder the terms:
-32a2q4 + 18a4 = 0

Solving
-32a2q4 + 18a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a2'.
2a2(-16q4 + 9a2) = 0

Factor a difference between two squares.
2a2((4q2 + 3a)(-4q2 + 3a)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}

Subproblem 2
Set the factor '(4q2 + 3a)' equal to zero and attempt to solve:

Simplifying
4q2 + 3a = 0

Reorder the terms:
3a + 4q2 = 0

Solving
3a + 4q2 = 0

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

Add '-4q2' to each side of the equation.
3a + 4q2 + -4q2 = 0 + -4q2

Combine like terms: 4q2 + -4q2 = 0
3a + 0 = 0 + -4q2
3a = 0 + -4q2
Remove the zero:
3a = -4q2

Divide each side by '3'.
a = -1.333333333q2

Simplifying
a = -1.333333333q2

Subproblem 3
Set the factor '(-4q2 + 3a)' equal to zero and attempt to solve:

Simplifying
-4q2 + 3a = 0

Reorder the terms:
3a + -4q2 = 0

Solving
3a + -4q2 = 0

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

Add '4q2' to each side of the equation.
3a + -4q2 + 4q2 = 0 + 4q2

Combine like terms: -4q2 + 4q2 = 0
3a + 0 = 0 + 4q2
3a = 0 + 4q2
Remove the zero:
3a = 4q2

Divide each side by '3'.
a = 1.333333333q2

Simplifying
a = 1.333333333q2
Solution
a = {0, -1.333333333q2, 1.333333333q2}

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