16(t^2)-192t-250=0

Solution for 16(t^2)-192t-250=0 equation:

Simplifying
16(t2) + -192t + -250 = 0

Reorder the terms:
-250 + -192t + 16t2 = 0

Solving
-250 + -192t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + -96t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-125 + -96t + 8t2)' equal to zero and attempt to solve:

Simplifying
-125 + -96t + 8t2 = 0

Solving
-125 + -96t + 8t2 = 0

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

Divide each side by '8'.
-15.625 + -12t + t2 = 0

Move the constant term to the right:

Add '15.625' to each side of the equation.
-15.625 + -12t + 15.625 + t2 = 0 + 15.625

Reorder the terms:
-15.625 + 15.625 + -12t + t2 = 0 + 15.625

Combine like terms: -15.625 + 15.625 = 0.000
0.000 + -12t + t2 = 0 + 15.625
-12t + t2 = 0 + 15.625

Combine like terms: 0 + 15.625 = 15.625
-12t + t2 = 15.625

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = 15.625 + 36

Reorder the terms:
36 + -12t + t2 = 15.625 + 36

Combine like terms: 15.625 + 36 = 51.625
36 + -12t + t2 = 51.625

Factor a perfect square on the left side:
(t + -6)(t + -6) = 51.625

Calculate the square root of the right side: 7.185053932

Break this problem into two subproblems by setting 
(t + -6) equal to 7.185053932 and -7.185053932.

Subproblem 1
t + -6 = 7.185053932

Simplifying
t + -6 = 7.185053932

Reorder the terms:
-6 + t = 7.185053932

Solving
-6 + t = 7.185053932

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = 7.185053932 + 6

Combine like terms: -6 + 6 = 0
0 + t = 7.185053932 + 6
t = 7.185053932 + 6

Combine like terms: 7.185053932 + 6 = 13.185053932
t = 13.185053932

Simplifying
t = 13.185053932

Subproblem 2
t + -6 = -7.185053932

Simplifying
t + -6 = -7.185053932

Reorder the terms:
-6 + t = -7.185053932

Solving
-6 + t = -7.185053932

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = -7.185053932 + 6

Combine like terms: -6 + 6 = 0
0 + t = -7.185053932 + 6
t = -7.185053932 + 6

Combine like terms: -7.185053932 + 6 = -1.185053932
t = -1.185053932

Simplifying
t = -1.185053932

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.185053932, -1.185053932}
Solution
t = {13.185053932, -1.185053932}