40=-16t^2-8t+120

Solution for 40=-16t^2-8t+120 equation:

Simplifying
40 = -16t2 + -8t + 120

Reorder the terms:
40 = 120 + -8t + -16t2

Solving
40 = 120 + -8t + -16t2

Solving for variable 't'.

Combine like terms: 40 + -120 = -80
-80 + 8t + 16t2 = 120 + -8t + -16t2 + -120 + 8t + 16t2

Reorder the terms:
-80 + 8t + 16t2 = 120 + -120 + -8t + 8t + -16t2 + 16t2

Combine like terms: 120 + -120 = 0
-80 + 8t + 16t2 = 0 + -8t + 8t + -16t2 + 16t2
-80 + 8t + 16t2 = -8t + 8t + -16t2 + 16t2

Combine like terms: -8t + 8t = 0
-80 + 8t + 16t2 = 0 + -16t2 + 16t2
-80 + 8t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-80 + 8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-10 + t + 2t2) = 0

Factor a trinomial.
8((-5 + -2t)(2 + -1t)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve:

Simplifying
-5 + -2t = 0

Solving
-5 + -2t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2t = 0 + 5
-2t = 0 + 5

Combine like terms: 0 + 5 = 5
-2t = 5

Divide each side by '-2'.
t = -2.5

Simplifying
t = -2.5
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-2.5, 2}