0=4t^2+8t-128

Solution for 0=4t^2+8t-128 equation:

Simplifying
0 = 4t2 + 8t + -128

Reorder the terms:
0 = -128 + 8t + 4t2

Solving
0 = -128 + 8t + 4t2

Solving for variable 't'.

Combine like terms: 0 + 128 = 128
128 + -8t + -4t2 = -128 + 8t + 4t2 + 128 + -8t + -4t2

Reorder the terms:
128 + -8t + -4t2 = -128 + 128 + 8t + -8t + 4t2 + -4t2

Combine like terms: -128 + 128 = 0
128 + -8t + -4t2 = 0 + 8t + -8t + 4t2 + -4t2
128 + -8t + -4t2 = 8t + -8t + 4t2 + -4t2

Combine like terms: 8t + -8t = 0
128 + -8t + -4t2 = 0 + 4t2 + -4t2
128 + -8t + -4t2 = 4t2 + -4t2

Combine like terms: 4t2 + -4t2 = 0
128 + -8t + -4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(32 + -2t + -1t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(32 + -2t + -1t2)' equal to zero and attempt to solve:

Simplifying
32 + -2t + -1t2 = 0

Solving
32 + -2t + -1t2 = 0

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

Divide each side by '-1'.
-32 + 2t + t2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 2t + 32 + t2 = 0 + 32

Reorder the terms:
-32 + 32 + 2t + t2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 2t + t2 = 0 + 32
2t + t2 = 0 + 32

Combine like terms: 0 + 32 = 32
2t + t2 = 32

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 32 + 1

Reorder the terms:
1 + 2t + t2 = 32 + 1

Combine like terms: 32 + 1 = 33
1 + 2t + t2 = 33

Factor a perfect square on the left side:
(t + 1)(t + 1) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(t + 1) equal to 5.744562647 and -5.744562647.

Subproblem 1
t + 1 = 5.744562647

Simplifying
t + 1 = 5.744562647

Reorder the terms:
1 + t = 5.744562647

Solving
1 + t = 5.744562647

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + t = 5.744562647 + -1
t = 5.744562647 + -1

Combine like terms: 5.744562647 + -1 = 4.744562647
t = 4.744562647

Simplifying
t = 4.744562647

Subproblem 2
t + 1 = -5.744562647

Simplifying
t + 1 = -5.744562647

Reorder the terms:
1 + t = -5.744562647

Solving
1 + t = -5.744562647

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -5.744562647 + -1

Combine like terms: 1 + -1 = 0
0 + t = -5.744562647 + -1
t = -5.744562647 + -1

Combine like terms: -5.744562647 + -1 = -6.744562647
t = -6.744562647

Simplifying
t = -6.744562647

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.744562647, -6.744562647}
Solution
t = {4.744562647, -6.744562647}