-16t^2-128t+240=0

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Solution for -16t^2-128t+240=0 equation: 


Simplifying
-16t2 + -128t + 240 = 0

Reorder the terms:
240 + -128t + -16t2 = 0

Solving
240 + -128t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(15 + -8t + -1t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(15 + -8t + -1t2)' equal to zero and attempt to solve:

Simplifying
15 + -8t + -1t2 = 0

Solving
15 + -8t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-15 + 8t + t2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8t + 15 + t2 = 0 + 15

Reorder the terms:
-15 + 15 + 8t + t2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8t + t2 = 0 + 15
8t + t2 = 0 + 15

Combine like terms: 0 + 15 = 15
8t + t2 = 15

The t term is 8t.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8t + 16 + t2 = 15 + 16

Reorder the terms:
16 + 8t + t2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + 8t + t2 = 31

Factor a perfect square on the left side:
(t + 4)(t + 4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(t + 4) equal to 5.567764363 and -5.567764363.


Subproblem 1
t + 4 = 5.567764363

Simplifying
t + 4 = 5.567764363

Reorder the terms:
4 + t = 5.567764363

Solving
4 + t = 5.567764363

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = 5.567764363 + -4

Combine like terms: 4 + -4 = 0
0 + t = 5.567764363 + -4
t = 5.567764363 + -4

Combine like terms: 5.567764363 + -4 = 1.567764363
t = 1.567764363

Simplifying
t = 1.567764363


Subproblem 2
t + 4 = -5.567764363

Simplifying
t + 4 = -5.567764363

Reorder the terms:
4 + t = -5.567764363

Solving
4 + t = -5.567764363

Solving for variable 't'.

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

Add '-4' to each side of the equation.
4 + -4 + t = -5.567764363 + -4

Combine like terms: 4 + -4 = 0
0 + t = -5.567764363 + -4
t = -5.567764363 + -4

Combine like terms: -5.567764363 + -4 = -9.567764363
t = -9.567764363

Simplifying
t = -9.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.567764363, -9.567764363}
Solution
t = {1.567764363, -9.567764363}

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