16t^2-64t-28=0

Solution for 16t^2-64t-28=0 equation:

Simplifying
16t2 + -64t + -28 = 0

Reorder the terms:
-28 + -64t + 16t2 = 0

Solving
-28 + -64t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-7 + -16t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -16t + 4t2)' equal to zero and attempt to solve:

Simplifying
-7 + -16t + 4t2 = 0

Solving
-7 + -16t + 4t2 = 0

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

Divide each side by '4'.
-1.75 + -4t + t2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -4t + 1.75 + t2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + -4t + t2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -4t + t2 = 0 + 1.75
-4t + t2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
-4t + t2 = 1.75

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 1.75 + 4

Reorder the terms:
4 + -4t + t2 = 1.75 + 4

Combine like terms: 1.75 + 4 = 5.75
4 + -4t + t2 = 5.75

Factor a perfect square on the left side:
(t + -2)(t + -2) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(t + -2) equal to 2.397915762 and -2.397915762.

Subproblem 1
t + -2 = 2.397915762

Simplifying
t + -2 = 2.397915762

Reorder the terms:
-2 + t = 2.397915762

Solving
-2 + t = 2.397915762

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 2.397915762 + 2

Combine like terms: -2 + 2 = 0
0 + t = 2.397915762 + 2
t = 2.397915762 + 2

Combine like terms: 2.397915762 + 2 = 4.397915762
t = 4.397915762

Simplifying
t = 4.397915762

Subproblem 2
t + -2 = -2.397915762

Simplifying
t + -2 = -2.397915762

Reorder the terms:
-2 + t = -2.397915762

Solving
-2 + t = -2.397915762

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -2.397915762 + 2

Combine like terms: -2 + 2 = 0
0 + t = -2.397915762 + 2
t = -2.397915762 + 2

Combine like terms: -2.397915762 + 2 = -0.397915762
t = -0.397915762

Simplifying
t = -0.397915762

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.397915762, -0.397915762}
Solution
t = {4.397915762, -0.397915762}