20=-16t^2+32t+100

Solution for 20=-16t^2+32t+100 equation:

Simplifying
20 = -16t2 + 32t + 100

Reorder the terms:
20 = 100 + 32t + -16t2

Solving
20 = 100 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 20 + -100 = -80
-80 + -32t + 16t2 = 100 + 32t + -16t2 + -100 + -32t + 16t2

Reorder the terms:
-80 + -32t + 16t2 = 100 + -100 + 32t + -32t + -16t2 + 16t2

Combine like terms: 100 + -100 = 0
-80 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-80 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-80 + -32t + 16t2 = 0 + -16t2 + 16t2
-80 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-80 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-5 + -2t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-5 + -2t + t2)' equal to zero and attempt to solve:

Simplifying
-5 + -2t + t2 = 0

Solving
-5 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + -2t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2t + t2 = 0 + 5
-2t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2t + t2 = 5

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 5 + 1

Reorder the terms:
1 + -2t + t2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2t + t2 = 6

Factor a perfect square on the left side:
(t + -1)(t + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(t + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
t + -1 = 2.449489743

Simplifying
t + -1 = 2.449489743

Reorder the terms:
-1 + t = 2.449489743

Solving
-1 + t = 2.449489743

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.449489743 + 1
t = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
t = 3.449489743

Simplifying
t = 3.449489743

Subproblem 2
t + -1 = -2.449489743

Simplifying
t + -1 = -2.449489743

Reorder the terms:
-1 + t = -2.449489743

Solving
-1 + t = -2.449489743

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.449489743 + 1
t = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
t = -1.449489743

Simplifying
t = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.449489743, -1.449489743}
Solution
t = {3.449489743, -1.449489743}