0=-16t^2+50t+6

Solution for 0=-16t^2+50t+6 equation:

Simplifying
0 = -16t2 + 50t + 6

Reorder the terms:
0 = 6 + 50t + -16t2

Solving
0 = 6 + 50t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -50t + 16t2 = 6 + 50t + -16t2 + -6 + -50t + 16t2

Reorder the terms:
-6 + -50t + 16t2 = 6 + -6 + 50t + -50t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + -50t + 16t2 = 0 + 50t + -50t + -16t2 + 16t2
-6 + -50t + 16t2 = 50t + -50t + -16t2 + 16t2

Combine like terms: 50t + -50t = 0
-6 + -50t + 16t2 = 0 + -16t2 + 16t2
-6 + -50t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -50t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -25t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -25t + 8t2)' equal to zero and attempt to solve:

Simplifying
-3 + -25t + 8t2 = 0

Solving
-3 + -25t + 8t2 = 0

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

Divide each side by '8'.
-0.375 + -3.125t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -3.125t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -3.125t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -3.125t + t2 = 0 + 0.375
-3.125t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-3.125t + t2 = 0.375

The t term is -3.125t.  Take half its coefficient (-1.5625).
Square it (2.44140625) and add it to both sides.

Add '2.44140625' to each side of the equation.
-3.125t + 2.44140625 + t2 = 0.375 + 2.44140625

Reorder the terms:
2.44140625 + -3.125t + t2 = 0.375 + 2.44140625

Combine like terms: 0.375 + 2.44140625 = 2.81640625
2.44140625 + -3.125t + t2 = 2.81640625

Factor a perfect square on the left side:
(t + -1.5625)(t + -1.5625) = 2.81640625

Calculate the square root of the right side: 1.678215198

Break this problem into two subproblems by setting 
(t + -1.5625) equal to 1.678215198 and -1.678215198.

Subproblem 1
t + -1.5625 = 1.678215198

Simplifying
t + -1.5625 = 1.678215198

Reorder the terms:
-1.5625 + t = 1.678215198

Solving
-1.5625 + t = 1.678215198

Solving for variable 't'.

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

Add '1.5625' to each side of the equation.
-1.5625 + 1.5625 + t = 1.678215198 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + t = 1.678215198 + 1.5625
t = 1.678215198 + 1.5625

Combine like terms: 1.678215198 + 1.5625 = 3.240715198
t = 3.240715198

Simplifying
t = 3.240715198

Subproblem 2
t + -1.5625 = -1.678215198

Simplifying
t + -1.5625 = -1.678215198

Reorder the terms:
-1.5625 + t = -1.678215198

Solving
-1.5625 + t = -1.678215198

Solving for variable 't'.

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

Add '1.5625' to each side of the equation.
-1.5625 + 1.5625 + t = -1.678215198 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + t = -1.678215198 + 1.5625
t = -1.678215198 + 1.5625

Combine like terms: -1.678215198 + 1.5625 = -0.115715198
t = -0.115715198

Simplifying
t = -0.115715198

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.240715198, -0.115715198}
Solution
t = {3.240715198, -0.115715198}