p^2+12p+6=0

Solution for p^2+12p+6=0 equation:

Simplifying
p2 + 12p + 6 = 0

Reorder the terms:
6 + 12p + p2 = 0

Solving
6 + 12p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 12p + -6 + p2 = 0 + -6

Reorder the terms:
6 + -6 + 12p + p2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12p + p2 = 0 + -6
12p + p2 = 0 + -6

Combine like terms: 0 + -6 = -6
12p + p2 = -6

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

Add '36' to each side of the equation.
12p + 36 + p2 = -6 + 36

Reorder the terms:
36 + 12p + p2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + 12p + p2 = 30

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

Calculate the square root of the right side: 5.477225575

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

Subproblem 1
p + 6 = 5.477225575

Simplifying
p + 6 = 5.477225575

Reorder the terms:
6 + p = 5.477225575

Solving
6 + p = 5.477225575

Solving for variable 'p'.

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

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

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

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

Simplifying
p = -0.522774425

Subproblem 2
p + 6 = -5.477225575

Simplifying
p + 6 = -5.477225575

Reorder the terms:
6 + p = -5.477225575

Solving
6 + p = -5.477225575

Solving for variable 'p'.

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

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

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

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

Simplifying
p = -11.477225575

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