140=-16t^2+48t+120

Solution for 140=-16t^2+48t+120 equation:

Simplifying
140 = -16t2 + 48t + 120

Reorder the terms:
140 = 120 + 48t + -16t2

Solving
140 = 120 + 48t + -16t2

Solving for variable 't'.

Combine like terms: 140 + -120 = 20
20 + -48t + 16t2 = 120 + 48t + -16t2 + -120 + -48t + 16t2

Reorder the terms:
20 + -48t + 16t2 = 120 + -120 + 48t + -48t + -16t2 + 16t2

Combine like terms: 120 + -120 = 0
20 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
20 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
20 + -48t + 16t2 = 0 + -16t2 + 16t2
20 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
20 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -12t + 4t2) = 0

Factor a trinomial.
4((1 + -2t)(5 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Subproblem 2
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
Solution
t = {0.5, 2.5}