-16t^2+60t+4=0

Solution for -16t^2+60t+4=0 equation:

Simplifying
-16t2 + 60t + 4 = 0

Reorder the terms:
4 + 60t + -16t2 = 0

Solving
4 + 60t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 15t + -4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 15t + -4t2)' equal to zero and attempt to solve:

Simplifying
1 + 15t + -4t2 = 0

Solving
1 + 15t + -4t2 = 0

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

Divide each side by '-4'.
-0.25 + -3.75t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -3.75t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -3.75t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -3.75t + t2 = 0 + 0.25
-3.75t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-3.75t + t2 = 0.25

The t term is -3.75t.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75t + 3.515625 + t2 = 0.25 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = 0.25 + 3.515625

Combine like terms: 0.25 + 3.515625 = 3.765625
3.515625 + -3.75t + t2 = 3.765625

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(t + -1.875) equal to 1.940521837 and -1.940521837.

Subproblem 1
t + -1.875 = 1.940521837

Simplifying
t + -1.875 = 1.940521837

Reorder the terms:
-1.875 + t = 1.940521837

Solving
-1.875 + t = 1.940521837

Solving for variable 't'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + t = 1.940521837 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = 1.940521837 + 1.875
t = 1.940521837 + 1.875

Combine like terms: 1.940521837 + 1.875 = 3.815521837
t = 3.815521837

Simplifying
t = 3.815521837

Subproblem 2
t + -1.875 = -1.940521837

Simplifying
t + -1.875 = -1.940521837

Reorder the terms:
-1.875 + t = -1.940521837

Solving
-1.875 + t = -1.940521837

Solving for variable 't'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + t = -1.940521837 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = -1.940521837 + 1.875
t = -1.940521837 + 1.875

Combine like terms: -1.940521837 + 1.875 = -0.065521837
t = -0.065521837

Simplifying
t = -0.065521837

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.815521837, -0.065521837}
Solution
t = {3.815521837, -0.065521837}