t=60+16t-t^2

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

Simplifying
t = 60 + 16t + -1t2

Solving
t = 60 + 16t + -1t2

Solving for variable 't'.

Reorder the terms:
-60 + t + -16t + t2 = 60 + 16t + -1t2 + -60 + -16t + t2

Combine like terms: t + -16t = -15t
-60 + -15t + t2 = 60 + 16t + -1t2 + -60 + -16t + t2

Reorder the terms:
-60 + -15t + t2 = 60 + -60 + 16t + -16t + -1t2 + t2

Combine like terms: 60 + -60 = 0
-60 + -15t + t2 = 0 + 16t + -16t + -1t2 + t2
-60 + -15t + t2 = 16t + -16t + -1t2 + t2

Combine like terms: 16t + -16t = 0
-60 + -15t + t2 = 0 + -1t2 + t2
-60 + -15t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-60 + -15t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -15t + 60 + t2 = 0 + 60

Reorder the terms:
-60 + 60 + -15t + t2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -15t + t2 = 0 + 60
-15t + t2 = 0 + 60

Combine like terms: 0 + 60 = 60
-15t + t2 = 60

The t term is -15t.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15t + 56.25 + t2 = 60 + 56.25

Reorder the terms:
56.25 + -15t + t2 = 60 + 56.25

Combine like terms: 60 + 56.25 = 116.25
56.25 + -15t + t2 = 116.25

Factor a perfect square on the left side:
(t + -7.5)(t + -7.5) = 116.25

Calculate the square root of the right side: 10.781929326

Break this problem into two subproblems by setting 
(t + -7.5) equal to 10.781929326 and -10.781929326.

Subproblem 1
t + -7.5 = 10.781929326

Simplifying
t + -7.5 = 10.781929326

Reorder the terms:
-7.5 + t = 10.781929326

Solving
-7.5 + t = 10.781929326

Solving for variable 't'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + t = 10.781929326 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + t = 10.781929326 + 7.5
t = 10.781929326 + 7.5

Combine like terms: 10.781929326 + 7.5 = 18.281929326
t = 18.281929326

Simplifying
t = 18.281929326

Subproblem 2
t + -7.5 = -10.781929326

Simplifying
t + -7.5 = -10.781929326

Reorder the terms:
-7.5 + t = -10.781929326

Solving
-7.5 + t = -10.781929326

Solving for variable 't'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + t = -10.781929326 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + t = -10.781929326 + 7.5
t = -10.781929326 + 7.5

Combine like terms: -10.781929326 + 7.5 = -3.281929326
t = -3.281929326

Simplifying
t = -3.281929326

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {18.281929326, -3.281929326}