-3a^2-27a-18=0

Solution for -3a^2-27a-18=0 equation:

Simplifying
-3a2 + -27a + -18 = 0

Reorder the terms:
-18 + -27a + -3a2 = 0

Solving
-18 + -27a + -3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6 + 9a + a2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(6 + 9a + a2)' equal to zero and attempt to solve:

Simplifying
6 + 9a + a2 = 0

Solving
6 + 9a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 9a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + 9a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 9a + a2 = 0 + -6
9a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
9a + a2 = -6

The a term is 9a.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9a + 20.25 + a2 = -6 + 20.25

Reorder the terms:
20.25 + 9a + a2 = -6 + 20.25

Combine like terms: -6 + 20.25 = 14.25
20.25 + 9a + a2 = 14.25

Factor a perfect square on the left side:
(a + 4.5)(a + 4.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(a + 4.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
a + 4.5 = 3.774917218

Simplifying
a + 4.5 = 3.774917218

Reorder the terms:
4.5 + a = 3.774917218

Solving
4.5 + a = 3.774917218

Solving for variable 'a'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + a = 3.774917218 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + a = 3.774917218 + -4.5
a = 3.774917218 + -4.5

Combine like terms: 3.774917218 + -4.5 = -0.725082782
a = -0.725082782

Simplifying
a = -0.725082782

Subproblem 2
a + 4.5 = -3.774917218

Simplifying
a + 4.5 = -3.774917218

Reorder the terms:
4.5 + a = -3.774917218

Solving
4.5 + a = -3.774917218

Solving for variable 'a'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + a = -3.774917218 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + a = -3.774917218 + -4.5
a = -3.774917218 + -4.5

Combine like terms: -3.774917218 + -4.5 = -8.274917218
a = -8.274917218

Simplifying
a = -8.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.725082782, -8.274917218}
Solution
a = {-0.725082782, -8.274917218}