0=-26t^2+48t+64

Solution for 0=-26t^2+48t+64 equation:

Simplifying
0 = -26t2 + 48t + 64

Reorder the terms:
0 = 64 + 48t + -26t2

Solving
0 = 64 + 48t + -26t2

Solving for variable 't'.

Combine like terms: 0 + -64 = -64
-64 + -48t + 26t2 = 64 + 48t + -26t2 + -64 + -48t + 26t2

Reorder the terms:
-64 + -48t + 26t2 = 64 + -64 + 48t + -48t + -26t2 + 26t2

Combine like terms: 64 + -64 = 0
-64 + -48t + 26t2 = 0 + 48t + -48t + -26t2 + 26t2
-64 + -48t + 26t2 = 48t + -48t + -26t2 + 26t2

Combine like terms: 48t + -48t = 0
-64 + -48t + 26t2 = 0 + -26t2 + 26t2
-64 + -48t + 26t2 = -26t2 + 26t2

Combine like terms: -26t2 + 26t2 = 0
-64 + -48t + 26t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -24t + 13t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-32 + -24t + 13t2)' equal to zero and attempt to solve:

Simplifying
-32 + -24t + 13t2 = 0

Solving
-32 + -24t + 13t2 = 0

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

Divide each side by '13'.
-2.461538462 + -1.846153846t + t2 = 0

Move the constant term to the right:

Add '2.461538462' to each side of the equation.
-2.461538462 + -1.846153846t + 2.461538462 + t2 = 0 + 2.461538462

Reorder the terms:
-2.461538462 + 2.461538462 + -1.846153846t + t2 = 0 + 2.461538462

Combine like terms: -2.461538462 + 2.461538462 = 0.000000000
0.000000000 + -1.846153846t + t2 = 0 + 2.461538462
-1.846153846t + t2 = 0 + 2.461538462

Combine like terms: 0 + 2.461538462 = 2.461538462
-1.846153846t + t2 = 2.461538462

The t term is -1.846153846t.  Take half its coefficient (-0.923076923).
Square it (0.8520710058) and add it to both sides.

Add '0.8520710058' to each side of the equation.
-1.846153846t + 0.8520710058 + t2 = 2.461538462 + 0.8520710058

Reorder the terms:
0.8520710058 + -1.846153846t + t2 = 2.461538462 + 0.8520710058

Combine like terms: 2.461538462 + 0.8520710058 = 3.3136094678
0.8520710058 + -1.846153846t + t2 = 3.3136094678

Factor a perfect square on the left side:
(t + -0.923076923)(t + -0.923076923) = 3.3136094678

Calculate the square root of the right side: 1.820332241

Break this problem into two subproblems by setting 
(t + -0.923076923) equal to 1.820332241 and -1.820332241.

Subproblem 1
t + -0.923076923 = 1.820332241

Simplifying
t + -0.923076923 = 1.820332241

Reorder the terms:
-0.923076923 + t = 1.820332241

Solving
-0.923076923 + t = 1.820332241

Solving for variable 't'.

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

Add '0.923076923' to each side of the equation.
-0.923076923 + 0.923076923 + t = 1.820332241 + 0.923076923

Combine like terms: -0.923076923 + 0.923076923 = 0.000000000
0.000000000 + t = 1.820332241 + 0.923076923
t = 1.820332241 + 0.923076923

Combine like terms: 1.820332241 + 0.923076923 = 2.743409164
t = 2.743409164

Simplifying
t = 2.743409164

Subproblem 2
t + -0.923076923 = -1.820332241

Simplifying
t + -0.923076923 = -1.820332241

Reorder the terms:
-0.923076923 + t = -1.820332241

Solving
-0.923076923 + t = -1.820332241

Solving for variable 't'.

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

Add '0.923076923' to each side of the equation.
-0.923076923 + 0.923076923 + t = -1.820332241 + 0.923076923

Combine like terms: -0.923076923 + 0.923076923 = 0.000000000
0.000000000 + t = -1.820332241 + 0.923076923
t = -1.820332241 + 0.923076923

Combine like terms: -1.820332241 + 0.923076923 = -0.897255318
t = -0.897255318

Simplifying
t = -0.897255318

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.743409164, -0.897255318}
Solution
t = {2.743409164, -0.897255318}