6t=.5t^2+16

Solution for 6t=.5t^2+16 equation:

Simplifying
6t = 0.5t2 + 16

Reorder the terms:
6t = 16 + 0.5t2

Solving
6t = 16 + 0.5t2

Solving for variable 't'.

Reorder the terms:
-16 + 6t + -0.5t2 = 16 + 0.5t2 + -16 + -0.5t2

Reorder the terms:
-16 + 6t + -0.5t2 = 16 + -16 + 0.5t2 + -0.5t2

Combine like terms: 16 + -16 = 0
-16 + 6t + -0.5t2 = 0 + 0.5t2 + -0.5t2
-16 + 6t + -0.5t2 = 0.5t2 + -0.5t2

Combine like terms: 0.5t2 + -0.5t2 = 0.0
-16 + 6t + -0.5t2 = 0.0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
32 + -12t + t2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -12t + -32 + t2 = 0 + -32

Reorder the terms:
32 + -32 + -12t + t2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -12t + t2 = 0 + -32
-12t + t2 = 0 + -32

Combine like terms: 0 + -32 = -32
-12t + t2 = -32

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -32 + 36

Reorder the terms:
36 + -12t + t2 = -32 + 36

Combine like terms: -32 + 36 = 4
36 + -12t + t2 = 4

Factor a perfect square on the left side:
(t + -6)(t + -6) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(t + -6) equal to 2 and -2.

Subproblem 1
t + -6 = 2

Simplifying
t + -6 = 2

Reorder the terms:
-6 + t = 2

Solving
-6 + t = 2

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = 2 + 6

Combine like terms: -6 + 6 = 0
0 + t = 2 + 6
t = 2 + 6

Combine like terms: 2 + 6 = 8
t = 8

Simplifying
t = 8

Subproblem 2
t + -6 = -2

Simplifying
t + -6 = -2

Reorder the terms:
-6 + t = -2

Solving
-6 + t = -2

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = -2 + 6

Combine like terms: -6 + 6 = 0
0 + t = -2 + 6
t = -2 + 6

Combine like terms: -2 + 6 = 4
t = 4

Simplifying
t = 4

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8, 4}