16a^5-81ab^4=0

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Solution for 16a^5-81ab^4=0 equation: 


Simplifying
16a5 + -81ab4 = 0

Reorder the terms:
-81ab4 + 16a5 = 0

Solving
-81ab4 + 16a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-81b4 + 16a4) = 0

Factor a difference between two squares.
a((9b2 + 4a2)(-9b2 + 4a2)) = 0

Factor a difference between two squares.
a((9b2 + 4a2)((3b + 2a)(-3b + 2a))) = 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 '(9b2 + 4a2)' equal to zero and attempt to solve:

Simplifying
9b2 + 4a2 = 0

Reorder the terms:
4a2 + 9b2 = 0

Solving
4a2 + 9b2 = 0

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

Add '-9b2' to each side of the equation.
4a2 + 9b2 + -9b2 = 0 + -9b2

Combine like terms: 9b2 + -9b2 = 0
4a2 + 0 = 0 + -9b2
4a2 = 0 + -9b2
Remove the zero:
4a2 = -9b2

Divide each side by '4'.
a2 = -2.25b2

Simplifying
a2 = -2.25b2

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 '(3b + 2a)' equal to zero and attempt to solve:

Simplifying
3b + 2a = 0

Reorder the terms:
2a + 3b = 0

Solving
2a + 3b = 0

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

Add '-3b' to each side of the equation.
2a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
2a + 0 = 0 + -3b
2a = 0 + -3b
Remove the zero:
2a = -3b

Divide each side by '2'.
a = -1.5b

Simplifying
a = -1.5b

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

Simplifying
-3b + 2a = 0

Reorder the terms:
2a + -3b = 0

Solving
2a + -3b = 0

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

Add '3b' to each side of the equation.
2a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
2a + 0 = 0 + 3b
2a = 0 + 3b
Remove the zero:
2a = 3b

Divide each side by '2'.
a = 1.5b

Simplifying
a = 1.5b
Solution
a = {0, -1.5b, 1.5b}

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