6=-16t^2+32t

Solution for 6=-16t^2+32t equation:

Simplifying
6 = -16t2 + 32t

Reorder the terms:
6 = 32t + -16t2

Solving
6 = 32t + -16t2

Solving for variable 't'.

Reorder the terms:
6 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
6 + -32t + 16t2 = 0 + -16t2 + 16t2
6 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
6 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -16t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -16t + 8t2)' equal to zero and attempt to solve:

Simplifying
3 + -16t + 8t2 = 0

Solving
3 + -16t + 8t2 = 0

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

Divide each side by '8'.
0.375 + -2t + t2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -2t + -0.375 + t2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -2t + t2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -2t + t2 = 0 + -0.375
-2t + t2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-2t + t2 = -0.375

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = -0.375 + 1

Reorder the terms:
1 + -2t + t2 = -0.375 + 1

Combine like terms: -0.375 + 1 = 0.625
1 + -2t + t2 = 0.625

Factor a perfect square on the left side:
(t + -1)(t + -1) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(t + -1) equal to 0.790569415 and -0.790569415.

Subproblem 1
t + -1 = 0.790569415

Simplifying
t + -1 = 0.790569415

Reorder the terms:
-1 + t = 0.790569415

Solving
-1 + t = 0.790569415

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + t = 0.790569415 + 1
t = 0.790569415 + 1

Combine like terms: 0.790569415 + 1 = 1.790569415
t = 1.790569415

Simplifying
t = 1.790569415

Subproblem 2
t + -1 = -0.790569415

Simplifying
t + -1 = -0.790569415

Reorder the terms:
-1 + t = -0.790569415

Solving
-1 + t = -0.790569415

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -0.790569415 + 1

Combine like terms: -1 + 1 = 0
0 + t = -0.790569415 + 1
t = -0.790569415 + 1

Combine like terms: -0.790569415 + 1 = 0.209430585
t = 0.209430585

Simplifying
t = 0.209430585

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.790569415, 0.209430585}
Solution
t = {1.790569415, 0.209430585}