-16t^2+2t+10=0

Solution for -16t^2+2t+10=0 equation:

Simplifying
-16t2 + 2t + 10 = 0

Reorder the terms:
10 + 2t + -16t2 = 0

Solving
10 + 2t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + t + -8t2)' equal to zero and attempt to solve:

Simplifying
5 + t + -8t2 = 0

Solving
5 + t + -8t2 = 0

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

Divide each side by '-8'.
-0.625 + -0.125t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -0.125t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -0.125t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -0.125t + t2 = 0 + 0.625
-0.125t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-0.125t + t2 = 0.625

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.125t + 0.25 + t2 = 0.625 + 0.25

Reorder the terms:
0.25 + -0.125t + t2 = 0.625 + 0.25

Combine like terms: 0.625 + 0.25 = 0.875
0.25 + -0.125t + t2 = 0.875

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(t + 0.5) equal to 0.935414347 and -0.935414347.

Subproblem 1
t + 0.5 = 0.935414347

Simplifying
t + 0.5 = 0.935414347

Reorder the terms:
0.5 + t = 0.935414347

Solving
0.5 + t = 0.935414347

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 0.935414347 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 0.935414347 + -0.5
t = 0.935414347 + -0.5

Combine like terms: 0.935414347 + -0.5 = 0.435414347
t = 0.435414347

Simplifying
t = 0.435414347

Subproblem 2
t + 0.5 = -0.935414347

Simplifying
t + 0.5 = -0.935414347

Reorder the terms:
0.5 + t = -0.935414347

Solving
0.5 + t = -0.935414347

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -0.935414347 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -0.935414347 + -0.5
t = -0.935414347 + -0.5

Combine like terms: -0.935414347 + -0.5 = -1.435414347
t = -1.435414347

Simplifying
t = -1.435414347

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.435414347, -1.435414347}
Solution
t = {0.435414347, -1.435414347}