6a^2+10a^6-3a^4=

Solution for 6a^2+10a^6-3a^4= equation:

Simplifying
6a2 + 10a6 + -3a4 = 0

Reorder the terms:
6a2 + -3a4 + 10a6 = 0

Solving
6a2 + -3a4 + 10a6 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}
Subproblem 2
Set the factor '(6 + -3a2 + 10a4)' equal to zero and attempt to solve:

Simplifying
6 + -3a2 + 10a4 = 0

Solving
6 + -3a2 + 10a4 = 0

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

Divide each side by '10'.
0.6 + -0.3a2 + a4 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + -0.3a2 + -0.6 + a4 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + -0.3a2 + a4 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + -0.3a2 + a4 = 0 + -0.6
-0.3a2 + a4 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
-0.3a2 + a4 = -0.6

The a term is -0.3a2.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3a2 + 0.0225 + a4 = -0.6 + 0.0225

Reorder the terms:
0.0225 + -0.3a2 + a4 = -0.6 + 0.0225

Combine like terms: -0.6 + 0.0225 = -0.5775
0.0225 + -0.3a2 + a4 = -0.5775

Factor a perfect square on the left side:
(a2 + -0.15)(a2 + -0.15) = -0.5775

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}