6(t)=-16t^2+46t+6

Solution for 6(t)=-16t^2+46t+6 equation:

Simplifying
6(t) = -16t2 + 46t + 6

Reorder the terms:
6t = 6 + 46t + -16t2

Solving
6t = 6 + 46t + -16t2

Solving for variable 't'.

Reorder the terms:
-6 + 6t + -46t + 16t2 = 6 + 46t + -16t2 + -6 + -46t + 16t2

Combine like terms: 6t + -46t = -40t
-6 + -40t + 16t2 = 6 + 46t + -16t2 + -6 + -46t + 16t2

Reorder the terms:
-6 + -40t + 16t2 = 6 + -6 + 46t + -46t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + -40t + 16t2 = 0 + 46t + -46t + -16t2 + 16t2
-6 + -40t + 16t2 = 46t + -46t + -16t2 + 16t2

Combine like terms: 46t + -46t = 0
-6 + -40t + 16t2 = 0 + -16t2 + 16t2
-6 + -40t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -40t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -20t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -20t + 8t2)' equal to zero and attempt to solve:

Simplifying
-3 + -20t + 8t2 = 0

Solving
-3 + -20t + 8t2 = 0

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

Divide each side by '8'.
-0.375 + -2.5t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -2.5t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -2.5t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -2.5t + t2 = 0 + 0.375
-2.5t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-2.5t + t2 = 0.375

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = 0.375 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = 0.375 + 1.5625

Combine like terms: 0.375 + 1.5625 = 1.9375
1.5625 + -2.5t + t2 = 1.9375

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 1.9375

Calculate the square root of the right side: 1.391941091

Break this problem into two subproblems by setting 
(t + -1.25) equal to 1.391941091 and -1.391941091.

Subproblem 1
t + -1.25 = 1.391941091

Simplifying
t + -1.25 = 1.391941091

Reorder the terms:
-1.25 + t = 1.391941091

Solving
-1.25 + t = 1.391941091

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = 1.391941091 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = 1.391941091 + 1.25
t = 1.391941091 + 1.25

Combine like terms: 1.391941091 + 1.25 = 2.641941091
t = 2.641941091

Simplifying
t = 2.641941091

Subproblem 2
t + -1.25 = -1.391941091

Simplifying
t + -1.25 = -1.391941091

Reorder the terms:
-1.25 + t = -1.391941091

Solving
-1.25 + t = -1.391941091

Solving for variable 't'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + t = -1.391941091 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + t = -1.391941091 + 1.25
t = -1.391941091 + 1.25

Combine like terms: -1.391941091 + 1.25 = -0.141941091
t = -0.141941091

Simplifying
t = -0.141941091

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.641941091, -0.141941091}
Solution
t = {2.641941091, -0.141941091}