0=-16t^2+32t+6

Solution for 0=-16t^2+32t+6 equation:

Simplifying
0 = -16t2 + 32t + 6

Reorder the terms:
0 = 6 + 32t + -16t2

Solving
0 = 6 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + -32t + 16t2 = 6 + 32t + -16t2 + -6 + -32t + 16t2

Reorder the terms:
-6 + -32t + 16t2 = 6 + -6 + 32t + -32t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-6 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-6 + -32t + 16t2 = 0 + -16t2 + 16t2
-6 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -16t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -16t + 8t2)' equal to zero and attempt to solve:

Simplifying
-3 + -16t + 8t2 = 0

Solving
-3 + -16t + 8t2 = 0

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

Divide each side by '8'.
-0.375 + -2t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -2t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -2t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -2t + t2 = 0 + 0.375
-2t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-2t + t2 = 0.375

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 = 0.375 + 1

Reorder the terms:
1 + -2t + t2 = 0.375 + 1

Combine like terms: 0.375 + 1 = 1.375
1 + -2t + t2 = 1.375

Factor a perfect square on the left side:
(t + -1)(t + -1) = 1.375

Calculate the square root of the right side: 1.17260394

Break this problem into two subproblems by setting 
(t + -1) equal to 1.17260394 and -1.17260394.

Subproblem 1
t + -1 = 1.17260394

Simplifying
t + -1 = 1.17260394

Reorder the terms:
-1 + t = 1.17260394

Solving
-1 + t = 1.17260394

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 = 1.17260394 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.17260394 + 1
t = 1.17260394 + 1

Combine like terms: 1.17260394 + 1 = 2.17260394
t = 2.17260394

Simplifying
t = 2.17260394

Subproblem 2
t + -1 = -1.17260394

Simplifying
t + -1 = -1.17260394

Reorder the terms:
-1 + t = -1.17260394

Solving
-1 + t = -1.17260394

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 = -1.17260394 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.17260394 + 1
t = -1.17260394 + 1

Combine like terms: -1.17260394 + 1 = -0.17260394
t = -0.17260394

Simplifying
t = -0.17260394

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.17260394, -0.17260394}
Solution
t = {2.17260394, -0.17260394}