t(t)=-16t+45t+6

Solution for t(t)=-16t+45t+6 equation:

Simplifying
t(t) = -16t + 45t + 6

Multiply t * t
t2 = -16t + 45t + 6

Reorder the terms:
t2 = 6 + -16t + 45t

Combine like terms: -16t + 45t = 29t
t2 = 6 + 29t

Solving
t2 = 6 + 29t

Solving for variable 't'.

Reorder the terms:
-6 + -29t + t2 = 6 + 29t + -6 + -29t

Reorder the terms:
-6 + -29t + t2 = 6 + -6 + 29t + -29t

Combine like terms: 6 + -6 = 0
-6 + -29t + t2 = 0 + 29t + -29t
-6 + -29t + t2 = 29t + -29t

Combine like terms: 29t + -29t = 0
-6 + -29t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -29t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -29t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -29t + t2 = 0 + 6
-29t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-29t + t2 = 6

The t term is -29t.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29t + 210.25 + t2 = 6 + 210.25

Reorder the terms:
210.25 + -29t + t2 = 6 + 210.25

Combine like terms: 6 + 210.25 = 216.25
210.25 + -29t + t2 = 216.25

Factor a perfect square on the left side:
(t + -14.5)(t + -14.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(t + -14.5) equal to 14.70544117 and -14.70544117.

Subproblem 1
t + -14.5 = 14.70544117

Simplifying
t + -14.5 = 14.70544117

Reorder the terms:
-14.5 + t = 14.70544117

Solving
-14.5 + t = 14.70544117

Solving for variable 't'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + t = 14.70544117 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + t = 14.70544117 + 14.5
t = 14.70544117 + 14.5

Combine like terms: 14.70544117 + 14.5 = 29.20544117
t = 29.20544117

Simplifying
t = 29.20544117

Subproblem 2
t + -14.5 = -14.70544117

Simplifying
t + -14.5 = -14.70544117

Reorder the terms:
-14.5 + t = -14.70544117

Solving
-14.5 + t = -14.70544117

Solving for variable 't'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + t = -14.70544117 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + t = -14.70544117 + 14.5
t = -14.70544117 + 14.5

Combine like terms: -14.70544117 + 14.5 = -0.20544117
t = -0.20544117

Simplifying
t = -0.20544117

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {29.20544117, -0.20544117}