20(t)=20-16t^2+32t

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

Simplifying
20(t) = 20 + -16t2 + 32t

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

Solving
20t = 20 + 32t + -16t2

Solving for variable 't'.

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

Combine like terms: 20t + -32t = -12t
-20 + -12t + 16t2 = 20 + 32t + -16t2 + -20 + -32t + 16t2

Reorder the terms:
-20 + -12t + 16t2 = 20 + -20 + 32t + -32t + -16t2 + 16t2

Combine like terms: 20 + -20 = 0
-20 + -12t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-20 + -12t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-20 + -12t + 16t2 = 0 + -16t2 + 16t2
-20 + -12t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-20 + -12t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -3t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -3t + 4t2)' equal to zero and attempt to solve:

Simplifying
-5 + -3t + 4t2 = 0

Solving
-5 + -3t + 4t2 = 0

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

Divide each side by '4'.
-1.25 + -0.75t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.75t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.75t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.75t + t2 = 0 + 1.25
-0.75t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.75t + t2 = 1.25

The t term is -0.75t.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75t + 0.140625 + t2 = 1.25 + 0.140625

Reorder the terms:
0.140625 + -0.75t + t2 = 1.25 + 0.140625

Combine like terms: 1.25 + 0.140625 = 1.390625
0.140625 + -0.75t + t2 = 1.390625

Factor a perfect square on the left side:
(t + -0.375)(t + -0.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(t + -0.375) equal to 1.179247642 and -1.179247642.

Subproblem 1
t + -0.375 = 1.179247642

Simplifying
t + -0.375 = 1.179247642

Reorder the terms:
-0.375 + t = 1.179247642

Solving
-0.375 + t = 1.179247642

Solving for variable 't'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + t = 1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + t = 1.179247642 + 0.375
t = 1.179247642 + 0.375

Combine like terms: 1.179247642 + 0.375 = 1.554247642
t = 1.554247642

Simplifying
t = 1.554247642

Subproblem 2
t + -0.375 = -1.179247642

Simplifying
t + -0.375 = -1.179247642

Reorder the terms:
-0.375 + t = -1.179247642

Solving
-0.375 + t = -1.179247642

Solving for variable 't'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + t = -1.179247642 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + t = -1.179247642 + 0.375
t = -1.179247642 + 0.375

Combine like terms: -1.179247642 + 0.375 = -0.804247642
t = -0.804247642

Simplifying
t = -0.804247642

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.554247642, -0.804247642}
Solution
t = {1.554247642, -0.804247642}