-16t^2+144t+20=0

Solution for -16t^2+144t+20=0 equation:

Simplifying
-16t2 + 144t + 20 = 0

Reorder the terms:
20 + 144t + -16t2 = 0

Solving
20 + 144t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 36t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + 36t + -4t2)' equal to zero and attempt to solve:

Simplifying
5 + 36t + -4t2 = 0

Solving
5 + 36t + -4t2 = 0

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

Divide each side by '-4'.
-1.25 + -9t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -9t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -9t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -9t + t2 = 0 + 1.25
-9t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-9t + t2 = 1.25

The t term is -9t.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9t + 20.25 + t2 = 1.25 + 20.25

Reorder the terms:
20.25 + -9t + t2 = 1.25 + 20.25

Combine like terms: 1.25 + 20.25 = 21.5
20.25 + -9t + t2 = 21.5

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 21.5

Calculate the square root of the right side: 4.636809248

Break this problem into two subproblems by setting 
(t + -4.5) equal to 4.636809248 and -4.636809248.

Subproblem 1
t + -4.5 = 4.636809248

Simplifying
t + -4.5 = 4.636809248

Reorder the terms:
-4.5 + t = 4.636809248

Solving
-4.5 + t = 4.636809248

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = 4.636809248 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 4.636809248 + 4.5
t = 4.636809248 + 4.5

Combine like terms: 4.636809248 + 4.5 = 9.136809248
t = 9.136809248

Simplifying
t = 9.136809248

Subproblem 2
t + -4.5 = -4.636809248

Simplifying
t + -4.5 = -4.636809248

Reorder the terms:
-4.5 + t = -4.636809248

Solving
-4.5 + t = -4.636809248

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = -4.636809248 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -4.636809248 + 4.5
t = -4.636809248 + 4.5

Combine like terms: -4.636809248 + 4.5 = -0.136809248
t = -0.136809248

Simplifying
t = -0.136809248

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.136809248, -0.136809248}
Solution
t = {9.136809248, -0.136809248}