80=-16t^2+88t

Solution for 80=-16t^2+88t equation:

Simplifying
80 = -16t2 + 88t

Reorder the terms:
80 = 88t + -16t2

Solving
80 = 88t + -16t2

Solving for variable 't'.

Reorder the terms:
80 + -88t + 16t2 = 88t + -88t + -16t2 + 16t2

Combine like terms: 88t + -88t = 0
80 + -88t + 16t2 = 0 + -16t2 + 16t2
80 + -88t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
80 + -88t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(10 + -11t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(10 + -11t + 2t2)' equal to zero and attempt to solve:

Simplifying
10 + -11t + 2t2 = 0

Solving
10 + -11t + 2t2 = 0

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

Divide each side by '2'.
5 + -5.5t + t2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5.5t + -5 + t2 = 0 + -5

Reorder the terms:
5 + -5 + -5.5t + t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5.5t + t2 = 0 + -5
-5.5t + t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5.5t + t2 = -5

The t term is -5.5t.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5t + 7.5625 + t2 = -5 + 7.5625

Reorder the terms:
7.5625 + -5.5t + t2 = -5 + 7.5625

Combine like terms: -5 + 7.5625 = 2.5625
7.5625 + -5.5t + t2 = 2.5625

Factor a perfect square on the left side:
(t + -2.75)(t + -2.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(t + -2.75) equal to 1.600781059 and -1.600781059.

Subproblem 1
t + -2.75 = 1.600781059

Simplifying
t + -2.75 = 1.600781059

Reorder the terms:
-2.75 + t = 1.600781059

Solving
-2.75 + t = 1.600781059

Solving for variable 't'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + t = 1.600781059 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + t = 1.600781059 + 2.75
t = 1.600781059 + 2.75

Combine like terms: 1.600781059 + 2.75 = 4.350781059
t = 4.350781059

Simplifying
t = 4.350781059

Subproblem 2
t + -2.75 = -1.600781059

Simplifying
t + -2.75 = -1.600781059

Reorder the terms:
-2.75 + t = -1.600781059

Solving
-2.75 + t = -1.600781059

Solving for variable 't'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + t = -1.600781059 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + t = -1.600781059 + 2.75
t = -1.600781059 + 2.75

Combine like terms: -1.600781059 + 2.75 = 1.149218941
t = 1.149218941

Simplifying
t = 1.149218941

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.350781059, 1.149218941}
Solution
t = {4.350781059, 1.149218941}