8(t)=-16t^2+22t+6

Solution for 8(t)=-16t^2+22t+6 equation:

Simplifying
8(t) = -16t2 + 22t + 6

Reorder the terms:
8t = 6 + 22t + -16t2

Solving
8t = 6 + 22t + -16t2

Solving for variable 't'.

Reorder the terms:
-6 + 8t + -22t + 16t2 = 6 + 22t + -16t2 + -6 + -22t + 16t2

Combine like terms: 8t + -22t = -14t
-6 + -14t + 16t2 = 6 + 22t + -16t2 + -6 + -22t + 16t2

Reorder the terms:
-6 + -14t + 16t2 = 6 + -6 + 22t + -22t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
-6 + -14t + 16t2 = 0 + 22t + -22t + -16t2 + 16t2
-6 + -14t + 16t2 = 22t + -22t + -16t2 + 16t2

Combine like terms: 22t + -22t = 0
-6 + -14t + 16t2 = 0 + -16t2 + 16t2
-6 + -14t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-6 + -14t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -7t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -7t + 8t2)' equal to zero and attempt to solve:

Simplifying
-3 + -7t + 8t2 = 0

Solving
-3 + -7t + 8t2 = 0

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

Divide each side by '8'.
-0.375 + -0.875t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.875t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.875t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.875t + t2 = 0 + 0.375
-0.875t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.875t + t2 = 0.375

The t term is -0.875t.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875t + 0.19140625 + t2 = 0.375 + 0.19140625

Reorder the terms:
0.19140625 + -0.875t + t2 = 0.375 + 0.19140625

Combine like terms: 0.375 + 0.19140625 = 0.56640625
0.19140625 + -0.875t + t2 = 0.56640625

Factor a perfect square on the left side:
(t + -0.4375)(t + -0.4375) = 0.56640625

Calculate the square root of the right side: 0.752599661

Break this problem into two subproblems by setting 
(t + -0.4375) equal to 0.752599661 and -0.752599661.

Subproblem 1
t + -0.4375 = 0.752599661

Simplifying
t + -0.4375 = 0.752599661

Reorder the terms:
-0.4375 + t = 0.752599661

Solving
-0.4375 + t = 0.752599661

Solving for variable 't'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + t = 0.752599661 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + t = 0.752599661 + 0.4375
t = 0.752599661 + 0.4375

Combine like terms: 0.752599661 + 0.4375 = 1.190099661
t = 1.190099661

Simplifying
t = 1.190099661

Subproblem 2
t + -0.4375 = -0.752599661

Simplifying
t + -0.4375 = -0.752599661

Reorder the terms:
-0.4375 + t = -0.752599661

Solving
-0.4375 + t = -0.752599661

Solving for variable 't'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + t = -0.752599661 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + t = -0.752599661 + 0.4375
t = -0.752599661 + 0.4375

Combine like terms: -0.752599661 + 0.4375 = -0.315099661
t = -0.315099661

Simplifying
t = -0.315099661

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.190099661, -0.315099661}
Solution
t = {1.190099661, -0.315099661}