180=-16t^2-2t+240

Solution for 180=-16t^2-2t+240 equation:

Simplifying
180 = -16t2 + -2t + 240

Reorder the terms:
180 = 240 + -2t + -16t2

Solving
180 = 240 + -2t + -16t2

Solving for variable 't'.

Combine like terms: 180 + -240 = -60
-60 + 2t + 16t2 = 240 + -2t + -16t2 + -240 + 2t + 16t2

Reorder the terms:
-60 + 2t + 16t2 = 240 + -240 + -2t + 2t + -16t2 + 16t2

Combine like terms: 240 + -240 = 0
-60 + 2t + 16t2 = 0 + -2t + 2t + -16t2 + 16t2
-60 + 2t + 16t2 = -2t + 2t + -16t2 + 16t2

Combine like terms: -2t + 2t = 0
-60 + 2t + 16t2 = 0 + -16t2 + 16t2
-60 + 2t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-60 + 2t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + t + 8t2) = 0

Factor a trinomial.
2((-2 + -1t)(15 + -8t)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(15 + -8t)' equal to zero and attempt to solve:

Simplifying
15 + -8t = 0

Solving
15 + -8t = 0

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

Add '-15' to each side of the equation.
15 + -15 + -8t = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -8t = 0 + -15
-8t = 0 + -15

Combine like terms: 0 + -15 = -15
-8t = -15

Divide each side by '-8'.
t = 1.875

Simplifying
t = 1.875
Solution
t = {-2, 1.875}