-16t^2+40t+4=0

Solution for -16t^2+40t+4=0 equation:

Simplifying
-16t2 + 40t + 4 = 0

Reorder the terms:
4 + 40t + -16t2 = 0

Solving
4 + 40t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 10t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 10t + -4t2)' equal to zero and attempt to solve:

Simplifying
1 + 10t + -4t2 = 0

Solving
1 + 10t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -2.5t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -2.5t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -2.5t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -2.5t + t2 = 0 + 0.25
-2.5t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-2.5t + t2 = 0.25

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = 0.25 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = 0.25 + 1.5625

Combine like terms: 0.25 + 1.5625 = 1.8125
1.5625 + -2.5t + t2 = 1.8125

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(t + -1.25) equal to 1.346291202 and -1.346291202.

Subproblem 1
t + -1.25 = 1.346291202

Simplifying
t + -1.25 = 1.346291202

Reorder the terms:
-1.25 + t = 1.346291202

Solving
-1.25 + t = 1.346291202

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 1.346291202 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 1.346291202 + 1.25
t = 1.346291202 + 1.25

Combine like terms: 1.346291202 + 1.25 = 2.596291202
t = 2.596291202

Simplifying
t = 2.596291202

Subproblem 2
t + -1.25 = -1.346291202

Simplifying
t + -1.25 = -1.346291202

Reorder the terms:
-1.25 + t = -1.346291202

Solving
-1.25 + t = -1.346291202

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -1.346291202 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -1.346291202 + 1.25
t = -1.346291202 + 1.25

Combine like terms: -1.346291202 + 1.25 = -0.096291202
t = -0.096291202

Simplifying
t = -0.096291202

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.596291202, -0.096291202}
Solution
t = {2.596291202, -0.096291202}