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

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


Simplifying
10a5 + 61a3b2 + 6ab4 = 0

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

Solving
6ab4 + 61a3b2 + 10a5 = 0

Solving for variable 'a'.

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

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

Simplifying
6b2 + a2 = 0

Reorder the terms:
a2 + 6b2 = 0

Solving
a2 + 6b2 = 0

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

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

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

Simplifying
a2 = -6b2

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 + 10a2)' equal to zero and attempt to solve:

Simplifying
b2 + 10a2 = 0

Reorder the terms:
10a2 + b2 = 0

Solving
10a2 + b2 = 0

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

Add '-1b2' to each side of the equation.
10a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
10a2 + 0 = 0 + -1b2
10a2 = 0 + -1b2
Remove the zero:
10a2 = -1b2

Divide each side by '10'.
a2 = -0.1b2

Simplifying
a2 = -0.1b2

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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