-16t^2+120t-20=0

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Solution for -16t^2+120t-20=0 equation: 


Simplifying
-16t2 + 120t + -20 = 0

Reorder the terms:
-20 + 120t + -16t2 = 0

Solving
-20 + 120t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 30t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-5 + 30t + -4t2)' equal to zero and attempt to solve:

Simplifying
-5 + 30t + -4t2 = 0

Solving
-5 + 30t + -4t2 = 0

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

Divide each side by '-4'.
1.25 + -7.5t + t2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -7.5t + -1.25 + t2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -7.5t + t2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -7.5t + t2 = 0 + -1.25
-7.5t + t2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-7.5t + t2 = -1.25

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = -1.25 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = -1.25 + 14.0625

Combine like terms: -1.25 + 14.0625 = 12.8125
14.0625 + -7.5t + t2 = 12.8125

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 12.8125

Calculate the square root of the right side: 3.579455266

Break this problem into two subproblems by setting 
(t + -3.75) equal to 3.579455266 and -3.579455266.


Subproblem 1
t + -3.75 = 3.579455266

Simplifying
t + -3.75 = 3.579455266

Reorder the terms:
-3.75 + t = 3.579455266

Solving
-3.75 + t = 3.579455266

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 3.579455266 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 3.579455266 + 3.75
t = 3.579455266 + 3.75

Combine like terms: 3.579455266 + 3.75 = 7.329455266
t = 7.329455266

Simplifying
t = 7.329455266


Subproblem 2
t + -3.75 = -3.579455266

Simplifying
t + -3.75 = -3.579455266

Reorder the terms:
-3.75 + t = -3.579455266

Solving
-3.75 + t = -3.579455266

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -3.579455266 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -3.579455266 + 3.75
t = -3.579455266 + 3.75

Combine like terms: -3.579455266 + 3.75 = 0.170544734
t = 0.170544734

Simplifying
t = 0.170544734


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.329455266, 0.170544734}
Solution
t = {7.329455266, 0.170544734}

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