-16t^2+12t+80=0

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Solution for -16t^2+12t+80=0 equation: 


Simplifying
-16t2 + 12t + 80 = 0

Reorder the terms:
80 + 12t + -16t2 = 0

Solving
80 + 12t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + 3t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + 3t + -4t2)' equal to zero and attempt to solve:

Simplifying
20 + 3t + -4t2 = 0

Solving
20 + 3t + -4t2 = 0

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

Divide each side by '-4'.
-5 + -0.75t + t2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.75t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.75t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.75t + t2 = 0 + 5
-0.75t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.75t + t2 = 5

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 = 5 + 0.140625

Reorder the terms:
0.140625 + -0.75t + t2 = 5 + 0.140625

Combine like terms: 5 + 0.140625 = 5.140625
0.140625 + -0.75t + t2 = 5.140625

Factor a perfect square on the left side:
(t + -0.375)(t + -0.375) = 5.140625

Calculate the square root of the right side: 2.267294643

Break this problem into two subproblems by setting 
(t + -0.375) equal to 2.267294643 and -2.267294643.


Subproblem 1
t + -0.375 = 2.267294643

Simplifying
t + -0.375 = 2.267294643

Reorder the terms:
-0.375 + t = 2.267294643

Solving
-0.375 + t = 2.267294643

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 = 2.267294643 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + t = 2.267294643 + 0.375
t = 2.267294643 + 0.375

Combine like terms: 2.267294643 + 0.375 = 2.642294643
t = 2.642294643

Simplifying
t = 2.642294643


Subproblem 2
t + -0.375 = -2.267294643

Simplifying
t + -0.375 = -2.267294643

Reorder the terms:
-0.375 + t = -2.267294643

Solving
-0.375 + t = -2.267294643

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 = -2.267294643 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + t = -2.267294643 + 0.375
t = -2.267294643 + 0.375

Combine like terms: -2.267294643 + 0.375 = -1.892294643
t = -1.892294643

Simplifying
t = -1.892294643


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.642294643, -1.892294643}
Solution
t = {2.642294643, -1.892294643}

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