-16t^2+32t+14=0

Solution for -16t^2+32t+14=0 equation:

Simplifying
-16t2 + 32t + 14 = 0

Reorder the terms:
14 + 32t + -16t2 = 0

Solving
14 + 32t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 16t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + 16t + -8t2)' equal to zero and attempt to solve:

Simplifying
7 + 16t + -8t2 = 0

Solving
7 + 16t + -8t2 = 0

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

Divide each side by '-8'.
-0.875 + -2t + t2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -2t + 0.875 + t2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -2t + t2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -2t + t2 = 0 + 0.875
-2t + t2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-2t + t2 = 0.875

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 = 0.875 + 1

Reorder the terms:
1 + -2t + t2 = 0.875 + 1

Combine like terms: 0.875 + 1 = 1.875
1 + -2t + t2 = 1.875

Factor a perfect square on the left side:
(t + -1)(t + -1) = 1.875

Calculate the square root of the right side: 1.369306394

Break this problem into two subproblems by setting 
(t + -1) equal to 1.369306394 and -1.369306394.

Subproblem 1
t + -1 = 1.369306394

Simplifying
t + -1 = 1.369306394

Reorder the terms:
-1 + t = 1.369306394

Solving
-1 + t = 1.369306394

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 = 1.369306394 + 1

Combine like terms: -1 + 1 = 0
0 + t = 1.369306394 + 1
t = 1.369306394 + 1

Combine like terms: 1.369306394 + 1 = 2.369306394
t = 2.369306394

Simplifying
t = 2.369306394

Subproblem 2
t + -1 = -1.369306394

Simplifying
t + -1 = -1.369306394

Reorder the terms:
-1 + t = -1.369306394

Solving
-1 + t = -1.369306394

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 = -1.369306394 + 1

Combine like terms: -1 + 1 = 0
0 + t = -1.369306394 + 1
t = -1.369306394 + 1

Combine like terms: -1.369306394 + 1 = -0.369306394
t = -0.369306394

Simplifying
t = -0.369306394

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.369306394, -0.369306394}
Solution
t = {2.369306394, -0.369306394}