-16t^2+80t-60=0

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Solution for -16t^2+80t-60=0 equation: 


Simplifying
-16t2 + 80t + -60 = 0

Reorder the terms:
-60 + 80t + -16t2 = 0

Solving
-60 + 80t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 20t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-15 + 20t + -4t2)' equal to zero and attempt to solve:

Simplifying
-15 + 20t + -4t2 = 0

Solving
-15 + 20t + -4t2 = 0

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

Divide each side by '-4'.
3.75 + -5t + t2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -5t + -3.75 + t2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -5t + t2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -5t + t2 = 0 + -3.75
-5t + t2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-5t + t2 = -3.75

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 = -3.75 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -3.75 + 6.25

Combine like terms: -3.75 + 6.25 = 2.5
6.25 + -5t + t2 = 2.5

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

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(t + -2.5) equal to 1.58113883 and -1.58113883.


Subproblem 1
t + -2.5 = 1.58113883

Simplifying
t + -2.5 = 1.58113883

Reorder the terms:
-2.5 + t = 1.58113883

Solving
-2.5 + t = 1.58113883

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 = 1.58113883 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 1.58113883 + 2.5
t = 1.58113883 + 2.5

Combine like terms: 1.58113883 + 2.5 = 4.08113883
t = 4.08113883

Simplifying
t = 4.08113883


Subproblem 2
t + -2.5 = -1.58113883

Simplifying
t + -2.5 = -1.58113883

Reorder the terms:
-2.5 + t = -1.58113883

Solving
-2.5 + t = -1.58113883

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 = -1.58113883 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -1.58113883 + 2.5
t = -1.58113883 + 2.5

Combine like terms: -1.58113883 + 2.5 = 0.91886117
t = 0.91886117

Simplifying
t = 0.91886117


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.08113883, 0.91886117}
Solution
t = {4.08113883, 0.91886117}

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