6a^5+61a^3b^2+10ab^4=0

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Solution for 6a^5+61a^3b^2+10ab^4=0 equation: 


Simplifying
6a5 + 61a3b2 + 10ab4 = 0

Reorder the terms:
10ab4 + 61a3b2 + 6a5 = 0

Solving
10ab4 + 61a3b2 + 6a5 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(10b4 + 61a2b2 + 6a4) = 0

Factor a trinomial.
a((10b2 + a2)(b2 + 6a2)) = 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 '(10b2 + a2)' equal to zero and attempt to solve:

Simplifying
10b2 + a2 = 0

Reorder the terms:
a2 + 10b2 = 0

Solving
a2 + 10b2 = 0

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

Add '-10b2' to each side of the equation.
a2 + 10b2 + -10b2 = 0 + -10b2

Combine like terms: 10b2 + -10b2 = 0
a2 + 0 = 0 + -10b2
a2 = 0 + -10b2
Remove the zero:
a2 = -10b2

Simplifying
a2 = -10b2

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 '(b2 + 6a2)' equal to zero and attempt to solve:

Simplifying
b2 + 6a2 = 0

Reorder the terms:
6a2 + b2 = 0

Solving
6a2 + b2 = 0

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

Add '-1b2' to each side of the equation.
6a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
6a2 + 0 = 0 + -1b2
6a2 = 0 + -1b2
Remove the zero:
6a2 = -1b2

Divide each side by '6'.
a2 = -0.1666666667b2

Simplifying
a2 = -0.1666666667b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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