16t^2-128t-192=0

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Solution for 16t^2-128t-192=0 equation: 


Simplifying
16t2 + -128t + -192 = 0

Reorder the terms:
-192 + -128t + 16t2 = 0

Solving
-192 + -128t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-12 + -8t + t2) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-12 + -8t + t2)' equal to zero and attempt to solve:

Simplifying
-12 + -8t + t2 = 0

Solving
-12 + -8t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8t + 12 + t2 = 0 + 12

Reorder the terms:
-12 + 12 + -8t + t2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8t + t2 = 0 + 12
-8t + t2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8t + t2 = 12

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 = 12 + 16

Reorder the terms:
16 + -8t + t2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + -8t + t2 = 28

Factor a perfect square on the left side:
(t + -4)(t + -4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(t + -4) equal to 5.291502622 and -5.291502622.


Subproblem 1
t + -4 = 5.291502622

Simplifying
t + -4 = 5.291502622

Reorder the terms:
-4 + t = 5.291502622

Solving
-4 + t = 5.291502622

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 = 5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + t = 5.291502622 + 4
t = 5.291502622 + 4

Combine like terms: 5.291502622 + 4 = 9.291502622
t = 9.291502622

Simplifying
t = 9.291502622


Subproblem 2
t + -4 = -5.291502622

Simplifying
t + -4 = -5.291502622

Reorder the terms:
-4 + t = -5.291502622

Solving
-4 + t = -5.291502622

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 = -5.291502622 + 4

Combine like terms: -4 + 4 = 0
0 + t = -5.291502622 + 4
t = -5.291502622 + 4

Combine like terms: -5.291502622 + 4 = -1.291502622
t = -1.291502622

Simplifying
t = -1.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.291502622, -1.291502622}
Solution
t = {9.291502622, -1.291502622}

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