-16t^2=8t+24

Solution for -16t^2=8t+24 equation:

Simplifying
-16t2 = 8t + 24

Reorder the terms:
-16t2 = 24 + 8t

Solving
-16t2 = 24 + 8t

Solving for variable 't'.

Reorder the terms:
-24 + -8t + -16t2 = 24 + 8t + -24 + -8t

Reorder the terms:
-24 + -8t + -16t2 = 24 + -24 + 8t + -8t

Combine like terms: 24 + -24 = 0
-24 + -8t + -16t2 = 0 + 8t + -8t
-24 + -8t + -16t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
-24 + -8t + -16t2 = 0

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

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

Simplifying
3 + t + 2t2 = 0

Solving
3 + t + 2t2 = 0

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

Divide each side by '2'.
1.5 + 0.5t + t2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.5t + -1.5 + t2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.5t + t2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.5t + t2 = 0 + -1.5
0.5t + t2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.5t + t2 = -1.5

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5t + 0.25 + t2 = -1.5 + 0.25

Reorder the terms:
0.25 + 0.5t + t2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + 0.5t + t2 = -1.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = -1.25

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.