0=2t^2+12t-16

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


Simplifying
0 = 2t2 + 12t + -16

Reorder the terms:
0 = -16 + 12t + 2t2

Solving
0 = -16 + 12t + 2t2

Solving for variable 't'.

Combine like terms: 0 + 16 = 16
16 + -12t + -2t2 = -16 + 12t + 2t2 + 16 + -12t + -2t2

Reorder the terms:
16 + -12t + -2t2 = -16 + 16 + 12t + -12t + 2t2 + -2t2

Combine like terms: -16 + 16 = 0
16 + -12t + -2t2 = 0 + 12t + -12t + 2t2 + -2t2
16 + -12t + -2t2 = 12t + -12t + 2t2 + -2t2

Combine like terms: 12t + -12t = 0
16 + -12t + -2t2 = 0 + 2t2 + -2t2
16 + -12t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
16 + -12t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -6t + -1t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -6t + -1t2)' equal to zero and attempt to solve:

Simplifying
8 + -6t + -1t2 = 0

Solving
8 + -6t + -1t2 = 0

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

Divide each side by '-1'.
-8 + 6t + t2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 6t + 8 + t2 = 0 + 8

Reorder the terms:
-8 + 8 + 6t + t2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 6t + t2 = 0 + 8
6t + t2 = 0 + 8

Combine like terms: 0 + 8 = 8
6t + t2 = 8

The t term is 6t.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6t + 9 + t2 = 8 + 9

Reorder the terms:
9 + 6t + t2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + 6t + t2 = 17

Factor a perfect square on the left side:
(t + 3)(t + 3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(t + 3) equal to 4.123105626 and -4.123105626.


Subproblem 1
t + 3 = 4.123105626

Simplifying
t + 3 = 4.123105626

Reorder the terms:
3 + t = 4.123105626

Solving
3 + t = 4.123105626

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = 4.123105626 + -3

Combine like terms: 3 + -3 = 0
0 + t = 4.123105626 + -3
t = 4.123105626 + -3

Combine like terms: 4.123105626 + -3 = 1.123105626
t = 1.123105626

Simplifying
t = 1.123105626


Subproblem 2
t + 3 = -4.123105626

Simplifying
t + 3 = -4.123105626

Reorder the terms:
3 + t = -4.123105626

Solving
3 + t = -4.123105626

Solving for variable 't'.

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

Add '-3' to each side of the equation.
3 + -3 + t = -4.123105626 + -3

Combine like terms: 3 + -3 = 0
0 + t = -4.123105626 + -3
t = -4.123105626 + -3

Combine like terms: -4.123105626 + -3 = -7.123105626
t = -7.123105626

Simplifying
t = -7.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.123105626, -7.123105626}
Solution
t = {1.123105626, -7.123105626}

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