=6t^2+12t+6-5

Solution for =6t^2+12t+6-5 equation:

Simplifying
0 = 6t2 + 12t + 6 + -5

Reorder the terms:
0 = 6 + -5 + 12t + 6t2

Combine like terms: 6 + -5 = 1
0 = 1 + 12t + 6t2

Solving
0 = 1 + 12t + 6t2

Solving for variable 't'.

Combine like terms: 0 + -1 = -1
-1 + -12t + -6t2 = 1 + 12t + 6t2 + -1 + -12t + -6t2

Reorder the terms:
-1 + -12t + -6t2 = 1 + -1 + 12t + -12t + 6t2 + -6t2

Combine like terms: 1 + -1 = 0
-1 + -12t + -6t2 = 0 + 12t + -12t + 6t2 + -6t2
-1 + -12t + -6t2 = 12t + -12t + 6t2 + -6t2

Combine like terms: 12t + -12t = 0
-1 + -12t + -6t2 = 0 + 6t2 + -6t2
-1 + -12t + -6t2 = 6t2 + -6t2

Combine like terms: 6t2 + -6t2 = 0
-1 + -12t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 12t + 6t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 12t + 6t2)' equal to zero and attempt to solve:

Simplifying
1 + 12t + 6t2 = 0

Solving
1 + 12t + 6t2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
0.1666666667 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 2t + -0.1666666667 + t2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 2t + t2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 2t + t2 = 0 + -0.1666666667
2t + t2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
2t + t2 = -0.1666666667

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = -0.1666666667 + 1

Reorder the terms:
1 + 2t + t2 = -0.1666666667 + 1

Combine like terms: -0.1666666667 + 1 = 0.8333333333
1 + 2t + t2 = 0.8333333333

Factor a perfect square on the left side:
(t + 1)(t + 1) = 0.8333333333

Calculate the square root of the right side: 0.912870929

Break this problem into two subproblems by setting 
(t + 1) equal to 0.912870929 and -0.912870929.

Subproblem 1
t + 1 = 0.912870929

Simplifying
t + 1 = 0.912870929

Reorder the terms:
1 + t = 0.912870929

Solving
1 + t = 0.912870929

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.912870929 + -1
t = 0.912870929 + -1

Combine like terms: 0.912870929 + -1 = -0.087129071
t = -0.087129071

Simplifying
t = -0.087129071

Subproblem 2
t + 1 = -0.912870929

Simplifying
t + 1 = -0.912870929

Reorder the terms:
1 + t = -0.912870929

Solving
1 + t = -0.912870929

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.912870929 + -1
t = -0.912870929 + -1

Combine like terms: -0.912870929 + -1 = -1.912870929
t = -1.912870929

Simplifying
t = -1.912870929

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.087129071, -1.912870929}
Solution
t = {-0.087129071, -1.912870929}