9a^4-a^2b^2=0

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Solution for 9a^4-a^2b^2=0 equation: 


Simplifying
9a4 + -1a2b2 = 0

Reorder the terms:
-1a2b2 + 9a4 = 0

Solving
-1a2b2 + 9a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a2'.
a2(-1b2 + 9a2) = 0

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


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 '(b + 3a)' equal to zero and attempt to solve:

Simplifying
b + 3a = 0

Reorder the terms:
3a + b = 0

Solving
3a + b = 0

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

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

Combine like terms: b + -1b = 0
3a + 0 = 0 + -1b
3a = 0 + -1b
Remove the zero:
3a = -1b

Divide each side by '3'.
a = -0.3333333333b

Simplifying
a = -0.3333333333b

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

Simplifying
-1b + 3a = 0

Reorder the terms:
3a + -1b = 0

Solving
3a + -1b = 0

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

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

Combine like terms: -1b + b = 0
3a + 0 = 0 + b
3a = 0 + b
Remove the zero:
3a = b

Divide each side by '3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b
Solution
a = {0, -0.3333333333b, 0.3333333333b}

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