6a^2+12a-72=-6

Solution for 6a^2+12a-72=-6 equation:

Simplifying
6a2 + 12a + -72 = -6

Reorder the terms:
-72 + 12a + 6a2 = -6

Solving
-72 + 12a + 6a2 = -6

Solving for variable 'a'.

Reorder the terms:
-72 + 6 + 12a + 6a2 = -6 + 6

Combine like terms: -72 + 6 = -66
-66 + 12a + 6a2 = -6 + 6

Combine like terms: -6 + 6 = 0
-66 + 12a + 6a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-11 + 2a + a2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-11 + 2a + a2)' equal to zero and attempt to solve:

Simplifying
-11 + 2a + a2 = 0

Solving
-11 + 2a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 2a + 11 + a2 = 0 + 11

Reorder the terms:
-11 + 11 + 2a + a2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2a + a2 = 0 + 11
2a + a2 = 0 + 11

Combine like terms: 0 + 11 = 11
2a + a2 = 11

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 = 11 + 1

Reorder the terms:
1 + 2a + a2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + 2a + a2 = 12

Factor a perfect square on the left side:
(a + 1)(a + 1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(a + 1) equal to 3.464101615 and -3.464101615.

Subproblem 1
a + 1 = 3.464101615

Simplifying
a + 1 = 3.464101615

Reorder the terms:
1 + a = 3.464101615

Solving
1 + a = 3.464101615

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 = 3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + a = 3.464101615 + -1
a = 3.464101615 + -1

Combine like terms: 3.464101615 + -1 = 2.464101615
a = 2.464101615

Simplifying
a = 2.464101615

Subproblem 2
a + 1 = -3.464101615

Simplifying
a + 1 = -3.464101615

Reorder the terms:
1 + a = -3.464101615

Solving
1 + a = -3.464101615

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 = -3.464101615 + -1

Combine like terms: 1 + -1 = 0
0 + a = -3.464101615 + -1
a = -3.464101615 + -1

Combine like terms: -3.464101615 + -1 = -4.464101615
a = -4.464101615

Simplifying
a = -4.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.464101615, -4.464101615}
Solution
a = {2.464101615, -4.464101615}