6a^8+10a^6-3a^4=

Solution for 6a^8+10a^6-3a^4= equation:

Simplifying
6a8 + 10a6 + -3a4 = 0

Reorder the terms:
-3a4 + 10a6 + 6a8 = 0

Solving
-3a4 + 10a6 + 6a8 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a4'.
a4(-3 + 10a2 + 6a4) = 0

Subproblem 1
Set the factor 'a4' equal to zero and attempt to solve:

Simplifying
a4 = 0

Solving
a4 = 0

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

Simplifying
a4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + 10a2 + 6a4)' equal to zero and attempt to solve:

Simplifying
-3 + 10a2 + 6a4 = 0

Solving
-3 + 10a2 + 6a4 = 0

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

Divide each side by '6'.
-0.5 + 1.666666667a2 + a4 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.666666667a2 + 0.5 + a4 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.666666667a2 + a4 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.666666667a2 + a4 = 0 + 0.5
1.666666667a2 + a4 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.666666667a2 + a4 = 0.5

The a term is 1.666666667a2.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667a2 + 0.6944444447 + a4 = 0.5 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667a2 + a4 = 0.5 + 0.6944444447

Combine like terms: 0.5 + 0.6944444447 = 1.1944444447
0.6944444447 + 1.666666667a2 + a4 = 1.1944444447

Factor a perfect square on the left side:
(a2 + 0.8333333335)(a2 + 0.8333333335) = 1.1944444447

Calculate the square root of the right side: 1.092906421

Break this problem into two subproblems by setting 
(a2 + 0.8333333335) equal to 1.092906421 and -1.092906421.

Subproblem 1
a2 + 0.8333333335 = 1.092906421

Simplifying
a2 + 0.8333333335 = 1.092906421

Reorder the terms:
0.8333333335 + a2 = 1.092906421

Solving
0.8333333335 + a2 = 1.092906421

Solving for variable 'a'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + a2 = 1.092906421 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + a2 = 1.092906421 + -0.8333333335
a2 = 1.092906421 + -0.8333333335

Combine like terms: 1.092906421 + -0.8333333335 = 0.2595730875
a2 = 0.2595730875

Simplifying
a2 = 0.2595730875

Take the square root of each side:
a = {-0.509483157, 0.509483157}

Subproblem 2
a2 + 0.8333333335 = -1.092906421

Simplifying
a2 + 0.8333333335 = -1.092906421

Reorder the terms:
0.8333333335 + a2 = -1.092906421

Solving
0.8333333335 + a2 = -1.092906421

Solving for variable 'a'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + a2 = -1.092906421 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + a2 = -1.092906421 + -0.8333333335
a2 = -1.092906421 + -0.8333333335

Combine like terms: -1.092906421 + -0.8333333335 = -1.9262397545
a2 = -1.9262397545

Simplifying
a2 = -1.9262397545

Reorder the terms:
1.9262397545 + a2 = -1.9262397545 + 1.9262397545

Combine like terms: -1.9262397545 + 1.9262397545 = 0.0000000000
1.9262397545 + a2 = 0.0000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.