2a^3+6a^2+6a=0

Solution for 2a^3+6a^2+6a=0 equation:

Simplifying
2a3 + 6a2 + 6a = 0

Reorder the terms:
6a + 6a2 + 2a3 = 0

Solving
6a + 6a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(3 + 3a + a2) = 0

Ignore the factor 2.
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 '(3 + 3a + a2)' equal to zero and attempt to solve:

Simplifying
3 + 3a + a2 = 0

Solving
3 + 3a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 3a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + 3a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3a + a2 = 0 + -3
3a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
3a + a2 = -3

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = -3 + 2.25

Reorder the terms:
2.25 + 3a + a2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + 3a + a2 = -0.75

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = -0.75

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}