-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((1 + -1t)(7 + 2t)) = 0

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

Divide each side by '-1'.
t = 1

Simplifying
t = 1
Subproblem 2
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
Solution
t = {1, -3.5}