-16t^2+140t-68=0

Solution for -16t^2+140t-68=0 equation:

Simplifying
-16t2 + 140t + -68 = 0

Reorder the terms:
-68 + 140t + -16t2 = 0

Solving
-68 + 140t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + 35t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-17 + 35t + -4t2)' equal to zero and attempt to solve:

Simplifying
-17 + 35t + -4t2 = 0

Solving
-17 + 35t + -4t2 = 0

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

Divide each side by '-4'.
4.25 + -8.75t + t2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + -8.75t + -4.25 + t2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + -8.75t + t2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + -8.75t + t2 = 0 + -4.25
-8.75t + t2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
-8.75t + t2 = -4.25

The t term is -8.75t.  Take half its coefficient (-4.375).
Square it (19.140625) and add it to both sides.

Add '19.140625' to each side of the equation.
-8.75t + 19.140625 + t2 = -4.25 + 19.140625

Reorder the terms:
19.140625 + -8.75t + t2 = -4.25 + 19.140625

Combine like terms: -4.25 + 19.140625 = 14.890625
19.140625 + -8.75t + t2 = 14.890625

Factor a perfect square on the left side:
(t + -4.375)(t + -4.375) = 14.890625

Calculate the square root of the right side: 3.85883726

Break this problem into two subproblems by setting 
(t + -4.375) equal to 3.85883726 and -3.85883726.

Subproblem 1
t + -4.375 = 3.85883726

Simplifying
t + -4.375 = 3.85883726

Reorder the terms:
-4.375 + t = 3.85883726

Solving
-4.375 + t = 3.85883726

Solving for variable 't'.

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

Add '4.375' to each side of the equation.
-4.375 + 4.375 + t = 3.85883726 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + t = 3.85883726 + 4.375
t = 3.85883726 + 4.375

Combine like terms: 3.85883726 + 4.375 = 8.23383726
t = 8.23383726

Simplifying
t = 8.23383726

Subproblem 2
t + -4.375 = -3.85883726

Simplifying
t + -4.375 = -3.85883726

Reorder the terms:
-4.375 + t = -3.85883726

Solving
-4.375 + t = -3.85883726

Solving for variable 't'.

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

Add '4.375' to each side of the equation.
-4.375 + 4.375 + t = -3.85883726 + 4.375

Combine like terms: -4.375 + 4.375 = 0.000
0.000 + t = -3.85883726 + 4.375
t = -3.85883726 + 4.375

Combine like terms: -3.85883726 + 4.375 = 0.51616274
t = 0.51616274

Simplifying
t = 0.51616274

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.23383726, 0.51616274}
Solution
t = {8.23383726, 0.51616274}