-3t^2-66t-111=0

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Solution for -3t^2-66t-111=0 equation: 


Simplifying
-3t2 + -66t + -111 = 0

Reorder the terms:
-111 + -66t + -3t2 = 0

Solving
-111 + -66t + -3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(37 + 22t + t2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(37 + 22t + t2)' equal to zero and attempt to solve:

Simplifying
37 + 22t + t2 = 0

Solving
37 + 22t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-37' to each side of the equation.
37 + 22t + -37 + t2 = 0 + -37

Reorder the terms:
37 + -37 + 22t + t2 = 0 + -37

Combine like terms: 37 + -37 = 0
0 + 22t + t2 = 0 + -37
22t + t2 = 0 + -37

Combine like terms: 0 + -37 = -37
22t + t2 = -37

The t term is 22t.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22t + 121 + t2 = -37 + 121

Reorder the terms:
121 + 22t + t2 = -37 + 121

Combine like terms: -37 + 121 = 84
121 + 22t + t2 = 84

Factor a perfect square on the left side:
(t + 11)(t + 11) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(t + 11) equal to 9.16515139 and -9.16515139.


Subproblem 1
t + 11 = 9.16515139

Simplifying
t + 11 = 9.16515139

Reorder the terms:
11 + t = 9.16515139

Solving
11 + t = 9.16515139

Solving for variable 't'.

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

Add '-11' to each side of the equation.
11 + -11 + t = 9.16515139 + -11

Combine like terms: 11 + -11 = 0
0 + t = 9.16515139 + -11
t = 9.16515139 + -11

Combine like terms: 9.16515139 + -11 = -1.83484861
t = -1.83484861

Simplifying
t = -1.83484861


Subproblem 2
t + 11 = -9.16515139

Simplifying
t + 11 = -9.16515139

Reorder the terms:
11 + t = -9.16515139

Solving
11 + t = -9.16515139

Solving for variable 't'.

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

Add '-11' to each side of the equation.
11 + -11 + t = -9.16515139 + -11

Combine like terms: 11 + -11 = 0
0 + t = -9.16515139 + -11
t = -9.16515139 + -11

Combine like terms: -9.16515139 + -11 = -20.16515139
t = -20.16515139

Simplifying
t = -20.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.83484861, -20.16515139}
Solution
t = {-1.83484861, -20.16515139}

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