24=-16t^2+32t+6

Solution for 24=-16t^2+32t+6 equation:

Simplifying
24 = -16t2 + 32t + 6

Reorder the terms:
24 = 6 + 32t + -16t2

Solving
24 = 6 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 24 + -6 = 18
18 + -32t + 16t2 = 6 + 32t + -16t2 + -6 + -32t + 16t2

Reorder the terms:
18 + -32t + 16t2 = 6 + -6 + 32t + -32t + -16t2 + 16t2

Combine like terms: 6 + -6 = 0
18 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
18 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
18 + -32t + 16t2 = 0 + -16t2 + 16t2
18 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
18 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -16t + 8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -16t + 8t2)' equal to zero and attempt to solve:

Simplifying
9 + -16t + 8t2 = 0

Solving
9 + -16t + 8t2 = 0

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

Divide each side by '8'.
1.125 + -2t + t2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + -2t + -1.125 + t2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + -2t + t2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + -2t + t2 = 0 + -1.125
-2t + t2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
-2t + t2 = -1.125

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 = -1.125 + 1

Reorder the terms:
1 + -2t + t2 = -1.125 + 1

Combine like terms: -1.125 + 1 = -0.125
1 + -2t + t2 = -0.125

Factor a perfect square on the left side:
(t + -1)(t + -1) = -0.125

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.