-16t^2+60t-7=0

Solution for -16t^2+60t-7=0 equation:

Simplifying
-16t2 + 60t + -7 = 0

Reorder the terms:
-7 + 60t + -16t2 = 0

Solving
-7 + 60t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.4375 + -3.75t + t2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + -3.75t + -0.4375 + t2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + -3.75t + t2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + -3.75t + t2 = 0 + -0.4375
-3.75t + t2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
-3.75t + t2 = -0.4375

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 = -0.4375 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = -0.4375 + 3.515625

Combine like terms: -0.4375 + 3.515625 = 3.078125
3.515625 + -3.75t + t2 = 3.078125

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 3.078125

Calculate the square root of the right side: 1.754458606

Break this problem into two subproblems by setting 
(t + -1.875) equal to 1.754458606 and -1.754458606.

Subproblem 1
t + -1.875 = 1.754458606

Simplifying
t + -1.875 = 1.754458606

Reorder the terms:
-1.875 + t = 1.754458606

Solving
-1.875 + t = 1.754458606

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 = 1.754458606 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = 1.754458606 + 1.875
t = 1.754458606 + 1.875

Combine like terms: 1.754458606 + 1.875 = 3.629458606
t = 3.629458606

Simplifying
t = 3.629458606

Subproblem 2
t + -1.875 = -1.754458606

Simplifying
t + -1.875 = -1.754458606

Reorder the terms:
-1.875 + t = -1.754458606

Solving
-1.875 + t = -1.754458606

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 = -1.754458606 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = -1.754458606 + 1.875
t = -1.754458606 + 1.875

Combine like terms: -1.754458606 + 1.875 = 0.120541394
t = 0.120541394

Simplifying
t = 0.120541394

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.629458606, 0.120541394}