16t^2+2t-20=0

Solution for 16t^2+2t-20=0 equation:

Simplifying
16t2 + 2t + -20 = 0

Reorder the terms:
-20 + 2t + 16t2 = 0

Solving
-20 + 2t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + t + 8t2)' equal to zero and attempt to solve:

Simplifying
-10 + t + 8t2 = 0

Solving
-10 + t + 8t2 = 0

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

Divide each side by '8'.
-1.25 + 0.125t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 0.125t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 0.125t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 0.125t + t2 = 0 + 1.25
0.125t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
0.125t + t2 = 1.25

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 = 1.25 + 0.25

Reorder the terms:
0.25 + 0.125t + t2 = 1.25 + 0.25

Combine like terms: 1.25 + 0.25 = 1.5
0.25 + 0.125t + t2 = 1.5

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.224744871 and -1.224744871.

Subproblem 1
t + 0.5 = 1.224744871

Simplifying
t + 0.5 = 1.224744871

Reorder the terms:
0.5 + t = 1.224744871

Solving
0.5 + t = 1.224744871

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 = 1.224744871 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 1.224744871 + -0.5
t = 1.224744871 + -0.5

Combine like terms: 1.224744871 + -0.5 = 0.724744871
t = 0.724744871

Simplifying
t = 0.724744871

Subproblem 2
t + 0.5 = -1.224744871

Simplifying
t + 0.5 = -1.224744871

Reorder the terms:
0.5 + t = -1.224744871

Solving
0.5 + t = -1.224744871

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 = -1.224744871 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -1.224744871 + -0.5
t = -1.224744871 + -0.5

Combine like terms: -1.224744871 + -0.5 = -1.724744871
t = -1.724744871

Simplifying
t = -1.724744871

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.724744871, -1.724744871}
Solution
t = {0.724744871, -1.724744871}