0=-26t^2+96t+12

Solution for 0=-26t^2+96t+12 equation:

Simplifying
0 = -26t2 + 96t + 12

Reorder the terms:
0 = 12 + 96t + -26t2

Solving
0 = 12 + 96t + -26t2

Solving for variable 't'.

Combine like terms: 0 + -12 = -12
-12 + -96t + 26t2 = 12 + 96t + -26t2 + -12 + -96t + 26t2

Reorder the terms:
-12 + -96t + 26t2 = 12 + -12 + 96t + -96t + -26t2 + 26t2

Combine like terms: 12 + -12 = 0
-12 + -96t + 26t2 = 0 + 96t + -96t + -26t2 + 26t2
-12 + -96t + 26t2 = 96t + -96t + -26t2 + 26t2

Combine like terms: 96t + -96t = 0
-12 + -96t + 26t2 = 0 + -26t2 + 26t2
-12 + -96t + 26t2 = -26t2 + 26t2

Combine like terms: -26t2 + 26t2 = 0
-12 + -96t + 26t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -48t + 13t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -48t + 13t2)' equal to zero and attempt to solve:

Simplifying
-6 + -48t + 13t2 = 0

Solving
-6 + -48t + 13t2 = 0

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

Divide each side by '13'.
-0.4615384615 + -3.692307692t + t2 = 0

Move the constant term to the right:

Add '0.4615384615' to each side of the equation.
-0.4615384615 + -3.692307692t + 0.4615384615 + t2 = 0 + 0.4615384615

Reorder the terms:
-0.4615384615 + 0.4615384615 + -3.692307692t + t2 = 0 + 0.4615384615

Combine like terms: -0.4615384615 + 0.4615384615 = 0.0000000000
0.0000000000 + -3.692307692t + t2 = 0 + 0.4615384615
-3.692307692t + t2 = 0 + 0.4615384615

Combine like terms: 0 + 0.4615384615 = 0.4615384615
-3.692307692t + t2 = 0.4615384615

The t term is -3.692307692t.  Take half its coefficient (-1.846153846).
Square it (3.408284023) and add it to both sides.

Add '3.408284023' to each side of the equation.
-3.692307692t + 3.408284023 + t2 = 0.4615384615 + 3.408284023

Reorder the terms:
3.408284023 + -3.692307692t + t2 = 0.4615384615 + 3.408284023

Combine like terms: 0.4615384615 + 3.408284023 = 3.8698224845
3.408284023 + -3.692307692t + t2 = 3.8698224845

Factor a perfect square on the left side:
(t + -1.846153846)(t + -1.846153846) = 3.8698224845

Calculate the square root of the right side: 1.967186439

Break this problem into two subproblems by setting 
(t + -1.846153846) equal to 1.967186439 and -1.967186439.

Subproblem 1
t + -1.846153846 = 1.967186439

Simplifying
t + -1.846153846 = 1.967186439

Reorder the terms:
-1.846153846 + t = 1.967186439

Solving
-1.846153846 + t = 1.967186439

Solving for variable 't'.

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

Add '1.846153846' to each side of the equation.
-1.846153846 + 1.846153846 + t = 1.967186439 + 1.846153846

Combine like terms: -1.846153846 + 1.846153846 = 0.000000000
0.000000000 + t = 1.967186439 + 1.846153846
t = 1.967186439 + 1.846153846

Combine like terms: 1.967186439 + 1.846153846 = 3.813340285
t = 3.813340285

Simplifying
t = 3.813340285

Subproblem 2
t + -1.846153846 = -1.967186439

Simplifying
t + -1.846153846 = -1.967186439

Reorder the terms:
-1.846153846 + t = -1.967186439

Solving
-1.846153846 + t = -1.967186439

Solving for variable 't'.

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

Add '1.846153846' to each side of the equation.
-1.846153846 + 1.846153846 + t = -1.967186439 + 1.846153846

Combine like terms: -1.846153846 + 1.846153846 = 0.000000000
0.000000000 + t = -1.967186439 + 1.846153846
t = -1.967186439 + 1.846153846

Combine like terms: -1.967186439 + 1.846153846 = -0.121032593
t = -0.121032593

Simplifying
t = -0.121032593

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.813340285, -0.121032593}
Solution
t = {3.813340285, -0.121032593}