-16t^2+80t-90=0

Solution for -16t^2+80t-90=0 equation:

Simplifying
-16t2 + 80t + -90 = 0

Reorder the terms:
-90 + 80t + -16t2 = 0

Solving
-90 + 80t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 40t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + 40t + -8t2)' equal to zero and attempt to solve:

Simplifying
-45 + 40t + -8t2 = 0

Solving
-45 + 40t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
5.625 + -5t + t2 = 0

Move the constant term to the right:

Add '-5.625' to each side of the equation.
5.625 + -5t + -5.625 + t2 = 0 + -5.625

Reorder the terms:
5.625 + -5.625 + -5t + t2 = 0 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + -5t + t2 = 0 + -5.625
-5t + t2 = 0 + -5.625

Combine like terms: 0 + -5.625 = -5.625
-5t + t2 = -5.625

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -5.625 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -5.625 + 6.25

Combine like terms: -5.625 + 6.25 = 0.625
6.25 + -5t + t2 = 0.625

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(t + -2.5) equal to 0.790569415 and -0.790569415.

Subproblem 1
t + -2.5 = 0.790569415

Simplifying
t + -2.5 = 0.790569415

Reorder the terms:
-2.5 + t = 0.790569415

Solving
-2.5 + t = 0.790569415

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 0.790569415 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 0.790569415 + 2.5
t = 0.790569415 + 2.5

Combine like terms: 0.790569415 + 2.5 = 3.290569415
t = 3.290569415

Simplifying
t = 3.290569415

Subproblem 2
t + -2.5 = -0.790569415

Simplifying
t + -2.5 = -0.790569415

Reorder the terms:
-2.5 + t = -0.790569415

Solving
-2.5 + t = -0.790569415

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -0.790569415 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -0.790569415 + 2.5
t = -0.790569415 + 2.5

Combine like terms: -0.790569415 + 2.5 = 1.709430585
t = 1.709430585

Simplifying
t = 1.709430585

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.290569415, 1.709430585}
Solution
t = {3.290569415, 1.709430585}