b^4a-81a^5=

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Solution for b^4a-81a^5= equation: 


Simplifying
b4a + -81a5 = 0

Solving
ab4 + -81a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(b4 + -81a4) = 0

Factor a difference between two squares.
a((b2 + 9a2)(b2 + -9a2)) = 0

Factor a difference between two squares.
a((b2 + 9a2)((b + 3a)(b + -3a))) = 0


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(b2 + 9a2)' equal to zero and attempt to solve:

Simplifying
b2 + 9a2 = 0

Reorder the terms:
9a2 + b2 = 0

Solving
9a2 + b2 = 0

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

Add '-1b2' to each side of the equation.
9a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
9a2 + 0 = 0 + -1b2
9a2 = 0 + -1b2
Remove the zero:
9a2 = -1b2

Divide each side by '9'.
a2 = -0.1111111111b2

Simplifying
a2 = -0.1111111111b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
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 4
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
Solution
a = {0, -0.3333333333b, 0.3333333333b}

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