-3x^2-36x-21=0

Solution for -3x^2-36x-21=0 equation:

Simplifying
-3x2 + -36x + -21 = 0

Reorder the terms:
-21 + -36x + -3x2 = 0

Solving
-21 + -36x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(7 + 12x + x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(7 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 12x + x2 = 0

Solving
7 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 12x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 12x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 12x + x2 = 0 + -7
12x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
12x + x2 = -7

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -7 + 36

Reorder the terms:
36 + 12x + x2 = -7 + 36

Combine like terms: -7 + 36 = 29
36 + 12x + x2 = 29

Factor a perfect square on the left side:
(x + 6)(x + 6) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + 6) equal to 5.385164807 and -5.385164807.

Subproblem 1
x + 6 = 5.385164807

Simplifying
x + 6 = 5.385164807

Reorder the terms:
6 + x = 5.385164807

Solving
6 + x = 5.385164807

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 5.385164807 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.385164807 + -6
x = 5.385164807 + -6

Combine like terms: 5.385164807 + -6 = -0.614835193
x = -0.614835193

Simplifying
x = -0.614835193

Subproblem 2
x + 6 = -5.385164807

Simplifying
x + 6 = -5.385164807

Reorder the terms:
6 + x = -5.385164807

Solving
6 + x = -5.385164807

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -5.385164807 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.385164807 + -6
x = -5.385164807 + -6

Combine like terms: -5.385164807 + -6 = -11.385164807
x = -11.385164807

Simplifying
x = -11.385164807

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.614835193, -11.385164807}
Solution
x = {-0.614835193, -11.385164807}