16T^2+129T-129=0

Solution for 16T^2+129T-129=0 equation:

Simplifying
16T2 + 129T + -129 = 0

Reorder the terms:
-129 + 129T + 16T2 = 0

Solving
-129 + 129T + 16T2 = 0

Solving for variable 'T'.

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

Divide each side by '16'.
-8.0625 + 8.0625T + T2 = 0

Move the constant term to the right:

Add '8.0625' to each side of the equation.
-8.0625 + 8.0625T + 8.0625 + T2 = 0 + 8.0625

Reorder the terms:
-8.0625 + 8.0625 + 8.0625T + T2 = 0 + 8.0625

Combine like terms: -8.0625 + 8.0625 = 0.0000
0.0000 + 8.0625T + T2 = 0 + 8.0625
8.0625T + T2 = 0 + 8.0625

Combine like terms: 0 + 8.0625 = 8.0625
8.0625T + T2 = 8.0625

The T term is 8.0625T.  Take half its coefficient (4.03125).
Square it (16.25097656) and add it to both sides.

Add '16.25097656' to each side of the equation.
8.0625T + 16.25097656 + T2 = 8.0625 + 16.25097656

Reorder the terms:
16.25097656 + 8.0625T + T2 = 8.0625 + 16.25097656

Combine like terms: 8.0625 + 16.25097656 = 24.31347656
16.25097656 + 8.0625T + T2 = 24.31347656

Factor a perfect square on the left side:
(T + 4.03125)(T + 4.03125) = 24.31347656

Calculate the square root of the right side: 4.930869757

Break this problem into two subproblems by setting 
(T + 4.03125) equal to 4.930869757 and -4.930869757.

Subproblem 1
T + 4.03125 = 4.930869757

Simplifying
T + 4.03125 = 4.930869757

Reorder the terms:
4.03125 + T = 4.930869757

Solving
4.03125 + T = 4.930869757

Solving for variable 'T'.

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

Add '-4.03125' to each side of the equation.
4.03125 + -4.03125 + T = 4.930869757 + -4.03125

Combine like terms: 4.03125 + -4.03125 = 0.00000
0.00000 + T = 4.930869757 + -4.03125
T = 4.930869757 + -4.03125

Combine like terms: 4.930869757 + -4.03125 = 0.899619757
T = 0.899619757

Simplifying
T = 0.899619757

Subproblem 2
T + 4.03125 = -4.930869757

Simplifying
T + 4.03125 = -4.930869757

Reorder the terms:
4.03125 + T = -4.930869757

Solving
4.03125 + T = -4.930869757

Solving for variable 'T'.

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

Add '-4.03125' to each side of the equation.
4.03125 + -4.03125 + T = -4.930869757 + -4.03125

Combine like terms: 4.03125 + -4.03125 = 0.00000
0.00000 + T = -4.930869757 + -4.03125
T = -4.930869757 + -4.03125

Combine like terms: -4.930869757 + -4.03125 = -8.962119757
T = -8.962119757

Simplifying
T = -8.962119757

Solution
The solution to the problem is based on the solutions
from the subproblems.
T = {0.899619757, -8.962119757}