-6=d^2+12d

Solution for -6=d^2+12d equation:

Simplifying
-6 = d2 + 12d

Reorder the terms:
-6 = 12d + d2

Solving
-6 = 12d + d2

Solving for variable 'd'.

Reorder the terms:
-6 + -12d + -1d2 = 12d + -12d + d2 + -1d2

Combine like terms: 12d + -12d = 0
-6 + -12d + -1d2 = 0 + d2 + -1d2
-6 + -12d + -1d2 = d2 + -1d2

Combine like terms: d2 + -1d2 = 0
-6 + -12d + -1d2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 12d + d2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 12d + d2)' equal to zero and attempt to solve:

Simplifying
6 + 12d + d2 = 0

Solving
6 + 12d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 12d + -6 + d2 = 0 + -6

Reorder the terms:
6 + -6 + 12d + d2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12d + d2 = 0 + -6
12d + d2 = 0 + -6

Combine like terms: 0 + -6 = -6
12d + d2 = -6

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

Add '36' to each side of the equation.
12d + 36 + d2 = -6 + 36

Reorder the terms:
36 + 12d + d2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + 12d + d2 = 30

Factor a perfect square on the left side:
(d + 6)(d + 6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(d + 6) equal to 5.477225575 and -5.477225575.

Subproblem 1
d + 6 = 5.477225575

Simplifying
d + 6 = 5.477225575

Reorder the terms:
6 + d = 5.477225575

Solving
6 + d = 5.477225575

Solving for variable 'd'.

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

Add '-6' to each side of the equation.
6 + -6 + d = 5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + d = 5.477225575 + -6
d = 5.477225575 + -6

Combine like terms: 5.477225575 + -6 = -0.522774425
d = -0.522774425

Simplifying
d = -0.522774425

Subproblem 2
d + 6 = -5.477225575

Simplifying
d + 6 = -5.477225575

Reorder the terms:
6 + d = -5.477225575

Solving
6 + d = -5.477225575

Solving for variable 'd'.

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

Add '-6' to each side of the equation.
6 + -6 + d = -5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + d = -5.477225575 + -6
d = -5.477225575 + -6

Combine like terms: -5.477225575 + -6 = -11.477225575
d = -11.477225575

Simplifying
d = -11.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.522774425, -11.477225575}
Solution
d = {-0.522774425, -11.477225575}