a^2+2a^2+2-6a-6-27=0

Solution for a^2+2a^2+2-6a-6-27=0 equation:

Simplifying
a2 + 2a2 + 2 + -6a + -6 + -27 = 0

Reorder the terms:
2 + -6 + -27 + -6a + a2 + 2a2 = 0

Combine like terms: 2 + -6 = -4
-4 + -27 + -6a + a2 + 2a2 = 0

Combine like terms: -4 + -27 = -31
-31 + -6a + a2 + 2a2 = 0

Combine like terms: a2 + 2a2 = 3a2
-31 + -6a + 3a2 = 0

Solving
-31 + -6a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
-10.33333333 + -2a + a2 = 0

Move the constant term to the right:

Add '10.33333333' to each side of the equation.
-10.33333333 + -2a + 10.33333333 + a2 = 0 + 10.33333333

Reorder the terms:
-10.33333333 + 10.33333333 + -2a + a2 = 0 + 10.33333333

Combine like terms: -10.33333333 + 10.33333333 = 0.00000000
0.00000000 + -2a + a2 = 0 + 10.33333333
-2a + a2 = 0 + 10.33333333

Combine like terms: 0 + 10.33333333 = 10.33333333
-2a + a2 = 10.33333333

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 = 10.33333333 + 1

Reorder the terms:
1 + -2a + a2 = 10.33333333 + 1

Combine like terms: 10.33333333 + 1 = 11.33333333
1 + -2a + a2 = 11.33333333

Factor a perfect square on the left side:
(a + -1)(a + -1) = 11.33333333

Calculate the square root of the right side: 3.366501646

Break this problem into two subproblems by setting 
(a + -1) equal to 3.366501646 and -3.366501646.

Subproblem 1
a + -1 = 3.366501646

Simplifying
a + -1 = 3.366501646

Reorder the terms:
-1 + a = 3.366501646

Solving
-1 + a = 3.366501646

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 = 3.366501646 + 1

Combine like terms: -1 + 1 = 0
0 + a = 3.366501646 + 1
a = 3.366501646 + 1

Combine like terms: 3.366501646 + 1 = 4.366501646
a = 4.366501646

Simplifying
a = 4.366501646

Subproblem 2
a + -1 = -3.366501646

Simplifying
a + -1 = -3.366501646

Reorder the terms:
-1 + a = -3.366501646

Solving
-1 + a = -3.366501646

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 = -3.366501646 + 1

Combine like terms: -1 + 1 = 0
0 + a = -3.366501646 + 1
a = -3.366501646 + 1

Combine like terms: -3.366501646 + 1 = -2.366501646
a = -2.366501646

Simplifying
a = -2.366501646

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {4.366501646, -2.366501646}