-16t^2+40t+80=24

Solution for -16t^2+40t+80=24 equation:

Simplifying
-16t2 + 40t + 80 = 24

Reorder the terms:
80 + 40t + -16t2 = 24

Solving
80 + 40t + -16t2 = 24

Solving for variable 't'.

Reorder the terms:
80 + -24 + 40t + -16t2 = 24 + -24

Combine like terms: 80 + -24 = 56
56 + 40t + -16t2 = 24 + -24

Combine like terms: 24 + -24 = 0
56 + 40t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(7 + 5t + -2t2) = 0

Factor a trinomial.
8((7 + -2t)(1 + t)) = 0

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

Simplifying
7 + -2t = 0

Solving
7 + -2t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2t = 0 + -7
-2t = 0 + -7

Combine like terms: 0 + -7 = -7
-2t = -7

Divide each side by '-2'.
t = 3.5

Simplifying
t = 3.5
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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 + -1

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

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

Simplifying
t = -1
Solution
t = {3.5, -1}