t^2+12t+6=0

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


Simplifying
t2 + 12t + 6 = 0

Reorder the terms:
6 + 12t + t2 = 0

Solving
6 + 12t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 12t + -6 + t2 = 0 + -6

Reorder the terms:
6 + -6 + 12t + t2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12t + t2 = 0 + -6
12t + t2 = 0 + -6

Combine like terms: 0 + -6 = -6
12t + t2 = -6

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

Add '36' to each side of the equation.
12t + 36 + t2 = -6 + 36

Reorder the terms:
36 + 12t + t2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + 12t + t2 = 30

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

Calculate the square root of the right side: 5.477225575

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


Subproblem 1
t + 6 = 5.477225575

Simplifying
t + 6 = 5.477225575

Reorder the terms:
6 + t = 5.477225575

Solving
6 + t = 5.477225575

Solving for variable 't'.

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

Add '-6' to each side of the equation.
6 + -6 + t = 5.477225575 + -6

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

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

Simplifying
t = -0.522774425


Subproblem 2
t + 6 = -5.477225575

Simplifying
t + 6 = -5.477225575

Reorder the terms:
6 + t = -5.477225575

Solving
6 + t = -5.477225575

Solving for variable 't'.

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

Add '-6' to each side of the equation.
6 + -6 + t = -5.477225575 + -6

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

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

Simplifying
t = -11.477225575


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

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