80=-16t^2+128t

Solution for 80=-16t^2+128t equation:

Simplifying
80 = -16t2 + 128t

Reorder the terms:
80 = 128t + -16t2

Solving
80 = 128t + -16t2

Solving for variable 't'.

Reorder the terms:
80 + -128t + 16t2 = 128t + -128t + -16t2 + 16t2

Combine like terms: 128t + -128t = 0
80 + -128t + 16t2 = 0 + -16t2 + 16t2
80 + -128t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
80 + -128t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(5 + -8t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(5 + -8t + t2)' equal to zero and attempt to solve:

Simplifying
5 + -8t + t2 = 0

Solving
5 + -8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8t + -5 + t2 = 0 + -5

Reorder the terms:
5 + -5 + -8t + t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8t + t2 = 0 + -5
-8t + t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8t + t2 = -5

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = -5 + 16

Reorder the terms:
16 + -8t + t2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8t + t2 = 11

Factor a perfect square on the left side:
(t + -4)(t + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(t + -4) equal to 3.31662479 and -3.31662479.

Subproblem 1
t + -4 = 3.31662479

Simplifying
t + -4 = 3.31662479

Reorder the terms:
-4 + t = 3.31662479

Solving
-4 + t = 3.31662479

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + t = 3.31662479 + 4
t = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
t = 7.31662479

Simplifying
t = 7.31662479

Subproblem 2
t + -4 = -3.31662479

Simplifying
t + -4 = -3.31662479

Reorder the terms:
-4 + t = -3.31662479

Solving
-4 + t = -3.31662479

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + t = -3.31662479 + 4
t = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
t = 0.68337521

Simplifying
t = 0.68337521

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.31662479, 0.68337521}
Solution
t = {7.31662479, 0.68337521}