16=2+38t-16t^2

Solution for 16=2+38t-16t^2 equation:

Simplifying
16 = 2 + 38t + -16t2

Solving
16 = 2 + 38t + -16t2

Solving for variable 't'.

Combine like terms: 16 + -2 = 14
14 + -38t + 16t2 = 2 + 38t + -16t2 + -2 + -38t + 16t2

Reorder the terms:
14 + -38t + 16t2 = 2 + -2 + 38t + -38t + -16t2 + 16t2

Combine like terms: 2 + -2 = 0
14 + -38t + 16t2 = 0 + 38t + -38t + -16t2 + 16t2
14 + -38t + 16t2 = 38t + -38t + -16t2 + 16t2

Combine like terms: 38t + -38t = 0
14 + -38t + 16t2 = 0 + -16t2 + 16t2
14 + -38t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
14 + -38t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -19t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -19t + 8t2)' equal to zero and attempt to solve:

Simplifying
7 + -19t + 8t2 = 0

Solving
7 + -19t + 8t2 = 0

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

Divide each side by '8'.
0.875 + -2.375t + t2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + -2.375t + -0.875 + t2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + -2.375t + t2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + -2.375t + t2 = 0 + -0.875
-2.375t + t2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
-2.375t + t2 = -0.875

The t term is -2.375t.  Take half its coefficient (-1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
-2.375t + 1.41015625 + t2 = -0.875 + 1.41015625

Reorder the terms:
1.41015625 + -2.375t + t2 = -0.875 + 1.41015625

Combine like terms: -0.875 + 1.41015625 = 0.53515625
1.41015625 + -2.375t + t2 = 0.53515625

Factor a perfect square on the left side:
(t + -1.1875)(t + -1.1875) = 0.53515625

Calculate the square root of the right side: 0.731543744

Break this problem into two subproblems by setting 
(t + -1.1875) equal to 0.731543744 and -0.731543744.

Subproblem 1
t + -1.1875 = 0.731543744

Simplifying
t + -1.1875 = 0.731543744

Reorder the terms:
-1.1875 + t = 0.731543744

Solving
-1.1875 + t = 0.731543744

Solving for variable 't'.

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

Add '1.1875' to each side of the equation.
-1.1875 + 1.1875 + t = 0.731543744 + 1.1875

Combine like terms: -1.1875 + 1.1875 = 0.0000
0.0000 + t = 0.731543744 + 1.1875
t = 0.731543744 + 1.1875

Combine like terms: 0.731543744 + 1.1875 = 1.919043744
t = 1.919043744

Simplifying
t = 1.919043744

Subproblem 2
t + -1.1875 = -0.731543744

Simplifying
t + -1.1875 = -0.731543744

Reorder the terms:
-1.1875 + t = -0.731543744

Solving
-1.1875 + t = -0.731543744

Solving for variable 't'.

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

Add '1.1875' to each side of the equation.
-1.1875 + 1.1875 + t = -0.731543744 + 1.1875

Combine like terms: -1.1875 + 1.1875 = 0.0000
0.0000 + t = -0.731543744 + 1.1875
t = -0.731543744 + 1.1875

Combine like terms: -0.731543744 + 1.1875 = 0.455956256
t = 0.455956256

Simplifying
t = 0.455956256

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.919043744, 0.455956256}
Solution
t = {1.919043744, 0.455956256}