162a^5-32ab^4=0

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Solution for 162a^5-32ab^4=0 equation: 


Simplifying
162a5 + -32ab4 = 0

Reorder the terms:
-32ab4 + 162a5 = 0

Solving
-32ab4 + 162a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-16b4 + 81a4) = 0

Factor a difference between two squares.
2a((4b2 + 9a2)(-4b2 + 9a2)) = 0

Factor a difference between two squares.
2a((4b2 + 9a2)((2b + 3a)(-2b + 3a))) = 0

Ignore the factor 2.

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 '(4b2 + 9a2)' equal to zero and attempt to solve:

Simplifying
4b2 + 9a2 = 0

Reorder the terms:
9a2 + 4b2 = 0

Solving
9a2 + 4b2 = 0

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

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

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

Divide each side by '9'.
a2 = -0.4444444444b2

Simplifying
a2 = -0.4444444444b2

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

Simplifying
2b + 3a = 0

Reorder the terms:
3a + 2b = 0

Solving
3a + 2b = 0

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

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

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

Divide each side by '3'.
a = -0.6666666667b

Simplifying
a = -0.6666666667b

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

Simplifying
-2b + 3a = 0

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

Solving
3a + -2b = 0

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

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

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

Divide each side by '3'.
a = 0.6666666667b

Simplifying
a = 0.6666666667b
Solution
a = {0, -0.6666666667b, 0.6666666667b}

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