3a^2+6a-6=0

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

Simplifying
3a2 + 6a + -6 = 0

Reorder the terms:
-6 + 6a + 3a2 = 0

Solving
-6 + 6a + 3a2 = 0

Solving for variable 'a'.

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 2a + a2)' equal to zero and attempt to solve:

Simplifying
-2 + 2a + a2 = 0

Solving
-2 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 2a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + 2a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 2a + a2 = 0 + 2
2a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
2a + a2 = 2

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 2 + 1

Reorder the terms:
1 + 2a + a2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + 2a + a2 = 3

Factor a perfect square on the left side:
(a + 1)(a + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(a + 1) equal to 1.732050808 and -1.732050808.

Subproblem 1
a + 1 = 1.732050808

Simplifying
a + 1 = 1.732050808

Reorder the terms:
1 + a = 1.732050808

Solving
1 + a = 1.732050808

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + a = 1.732050808 + -1
a = 1.732050808 + -1

Combine like terms: 1.732050808 + -1 = 0.732050808
a = 0.732050808

Simplifying
a = 0.732050808

Subproblem 2
a + 1 = -1.732050808

Simplifying
a + 1 = -1.732050808

Reorder the terms:
1 + a = -1.732050808

Solving
1 + a = -1.732050808

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + a = -1.732050808 + -1
a = -1.732050808 + -1

Combine like terms: -1.732050808 + -1 = -2.732050808
a = -2.732050808

Simplifying
a = -2.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.732050808, -2.732050808}
Solution
a = {0.732050808, -2.732050808}