-6a^7+3a^4-a=

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Solution for -6a^7+3a^4-a= equation: 


Simplifying
-6a7 + 3a4 + -1a = 0

Reorder the terms:
-1a + 3a4 + -6a7 = 0

Solving
-1a + 3a4 + -6a7 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + 3a3 + -6a6) = 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 '(-1 + 3a3 + -6a6)' equal to zero and attempt to solve:

Simplifying
-1 + 3a3 + -6a6 = 0

Solving
-1 + 3a3 + -6a6 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
0.1666666667 + -0.5a3 + a6 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.5a3 + -0.1666666667 + a6 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -0.5a3 + a6 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -0.5a3 + a6 = 0 + -0.1666666667
-0.5a3 + a6 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-0.5a3 + a6 = -0.1666666667

The a term is -0.5a3.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5a3 + 0.0625 + a6 = -0.1666666667 + 0.0625

Reorder the terms:
0.0625 + -0.5a3 + a6 = -0.1666666667 + 0.0625

Combine like terms: -0.1666666667 + 0.0625 = -0.1041666667
0.0625 + -0.5a3 + a6 = -0.1041666667

Factor a perfect square on the left side:
(a3 + -0.25)(a3 + -0.25) = -0.1041666667

Can't calculate square root of the right side.

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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