0=116t^2+64t-60

Solution for 0=116t^2+64t-60 equation:

Simplifying
0 = 116t2 + 64t + -60

Reorder the terms:
0 = -60 + 64t + 116t2

Solving
0 = -60 + 64t + 116t2

Solving for variable 't'.

Combine like terms: 0 + 60 = 60
60 + -64t + -116t2 = -60 + 64t + 116t2 + 60 + -64t + -116t2

Reorder the terms:
60 + -64t + -116t2 = -60 + 60 + 64t + -64t + 116t2 + -116t2

Combine like terms: -60 + 60 = 0
60 + -64t + -116t2 = 0 + 64t + -64t + 116t2 + -116t2
60 + -64t + -116t2 = 64t + -64t + 116t2 + -116t2

Combine like terms: 64t + -64t = 0
60 + -64t + -116t2 = 0 + 116t2 + -116t2
60 + -64t + -116t2 = 116t2 + -116t2

Combine like terms: 116t2 + -116t2 = 0
60 + -64t + -116t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -16t + -29t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(15 + -16t + -29t2)' equal to zero and attempt to solve:

Simplifying
15 + -16t + -29t2 = 0

Solving
15 + -16t + -29t2 = 0

Begin completing the square.  Divide all terms by
-29 the coefficient of the squared term: 

Divide each side by '-29'.
-0.5172413793 + 0.5517241379t + t2 = 0

Move the constant term to the right:

Add '0.5172413793' to each side of the equation.
-0.5172413793 + 0.5517241379t + 0.5172413793 + t2 = 0 + 0.5172413793

Reorder the terms:
-0.5172413793 + 0.5172413793 + 0.5517241379t + t2 = 0 + 0.5172413793

Combine like terms: -0.5172413793 + 0.5172413793 = 0.0000000000
0.0000000000 + 0.5517241379t + t2 = 0 + 0.5172413793
0.5517241379t + t2 = 0 + 0.5172413793

Combine like terms: 0 + 0.5172413793 = 0.5172413793
0.5517241379t + t2 = 0.5172413793

The t term is 0.5517241379t.  Take half its coefficient (0.275862069).
Square it (0.07609988111) and add it to both sides.

Add '0.07609988111' to each side of the equation.
0.5517241379t + 0.07609988111 + t2 = 0.5172413793 + 0.07609988111

Reorder the terms:
0.07609988111 + 0.5517241379t + t2 = 0.5172413793 + 0.07609988111

Combine like terms: 0.5172413793 + 0.07609988111 = 0.59334126041
0.07609988111 + 0.5517241379t + t2 = 0.59334126041

Factor a perfect square on the left side:
(t + 0.275862069)(t + 0.275862069) = 0.59334126041

Calculate the square root of the right side: 0.770286479

Break this problem into two subproblems by setting 
(t + 0.275862069) equal to 0.770286479 and -0.770286479.

Subproblem 1
t + 0.275862069 = 0.770286479

Simplifying
t + 0.275862069 = 0.770286479

Reorder the terms:
0.275862069 + t = 0.770286479

Solving
0.275862069 + t = 0.770286479

Solving for variable 't'.

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

Add '-0.275862069' to each side of the equation.
0.275862069 + -0.275862069 + t = 0.770286479 + -0.275862069

Combine like terms: 0.275862069 + -0.275862069 = 0.000000000
0.000000000 + t = 0.770286479 + -0.275862069
t = 0.770286479 + -0.275862069

Combine like terms: 0.770286479 + -0.275862069 = 0.49442441
t = 0.49442441

Simplifying
t = 0.49442441

Subproblem 2
t + 0.275862069 = -0.770286479

Simplifying
t + 0.275862069 = -0.770286479

Reorder the terms:
0.275862069 + t = -0.770286479

Solving
0.275862069 + t = -0.770286479

Solving for variable 't'.

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

Add '-0.275862069' to each side of the equation.
0.275862069 + -0.275862069 + t = -0.770286479 + -0.275862069

Combine like terms: 0.275862069 + -0.275862069 = 0.000000000
0.000000000 + t = -0.770286479 + -0.275862069
t = -0.770286479 + -0.275862069

Combine like terms: -0.770286479 + -0.275862069 = -1.046148548
t = -1.046148548

Simplifying
t = -1.046148548

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.49442441, -1.046148548}
Solution
t = {0.49442441, -1.046148548}