0=-16t^2+60t-6

Solution for 0=-16t^2+60t-6 equation:

Simplifying
0 = -16t2 + 60t + -6

Reorder the terms:
0 = -6 + 60t + -16t2

Solving
0 = -6 + 60t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 6 = 6
6 + -60t + 16t2 = -6 + 60t + -16t2 + 6 + -60t + 16t2

Reorder the terms:
6 + -60t + 16t2 = -6 + 6 + 60t + -60t + -16t2 + 16t2

Combine like terms: -6 + 6 = 0
6 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2
6 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2

Combine like terms: 60t + -60t = 0
6 + -60t + 16t2 = 0 + -16t2 + 16t2
6 + -60t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
6 + -60t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -30t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -30t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + -30t + 8t2 = 0

Solving
3 + -30t + 8t2 = 0

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

Divide each side by '8'.
0.375 + -3.75t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -3.75t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -3.75t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -3.75t + t2 = 0 + -0.375
-3.75t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-3.75t + t2 = -0.375

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 = -0.375 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = -0.375 + 3.515625

Combine like terms: -0.375 + 3.515625 = 3.140625
3.515625 + -3.75t + t2 = 3.140625

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 3.140625

Calculate the square root of the right side: 1.77218086

Break this problem into two subproblems by setting 
(t + -1.875) equal to 1.77218086 and -1.77218086.

Subproblem 1
t + -1.875 = 1.77218086

Simplifying
t + -1.875 = 1.77218086

Reorder the terms:
-1.875 + t = 1.77218086

Solving
-1.875 + t = 1.77218086

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 = 1.77218086 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = 1.77218086 + 1.875
t = 1.77218086 + 1.875

Combine like terms: 1.77218086 + 1.875 = 3.64718086
t = 3.64718086

Simplifying
t = 3.64718086

Subproblem 2
t + -1.875 = -1.77218086

Simplifying
t + -1.875 = -1.77218086

Reorder the terms:
-1.875 + t = -1.77218086

Solving
-1.875 + t = -1.77218086

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 = -1.77218086 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = -1.77218086 + 1.875
t = -1.77218086 + 1.875

Combine like terms: -1.77218086 + 1.875 = 0.10281914
t = 0.10281914

Simplifying
t = 0.10281914

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.64718086, 0.10281914}
Solution
t = {3.64718086, 0.10281914}