-206=16t^2+32t

Solution for -206=16t^2+32t equation:

Simplifying
-206 = 16t2 + 32t

Reorder the terms:
-206 = 32t + 16t2

Solving
-206 = 32t + 16t2

Solving for variable 't'.

Reorder the terms:
-206 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
-206 + -32t + -16t2 = 0 + 16t2 + -16t2
-206 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
-206 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(103 + 16t + 8t2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(103 + 16t + 8t2)' equal to zero and attempt to solve:

Simplifying
103 + 16t + 8t2 = 0

Solving
103 + 16t + 8t2 = 0

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

Divide each side by '8'.
12.875 + 2t + t2 = 0

Move the constant term to the right:

Add '-12.875' to each side of the equation.
12.875 + 2t + -12.875 + t2 = 0 + -12.875

Reorder the terms:
12.875 + -12.875 + 2t + t2 = 0 + -12.875

Combine like terms: 12.875 + -12.875 = 0.000
0.000 + 2t + t2 = 0 + -12.875
2t + t2 = 0 + -12.875

Combine like terms: 0 + -12.875 = -12.875
2t + t2 = -12.875

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 = -12.875 + 1

Reorder the terms:
1 + 2t + t2 = -12.875 + 1

Combine like terms: -12.875 + 1 = -11.875
1 + 2t + t2 = -11.875

Factor a perfect square on the left side:
(t + 1)(t + 1) = -11.875

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.