0=-32t^2-64t+480

Solution for 0=-32t^2-64t+480 equation:

Simplifying
0 = -32t2 + -64t + 480

Reorder the terms:
0 = 480 + -64t + -32t2

Solving
0 = 480 + -64t + -32t2

Solving for variable 't'.

Combine like terms: 0 + -480 = -480
-480 + 64t + 32t2 = 480 + -64t + -32t2 + -480 + 64t + 32t2

Reorder the terms:
-480 + 64t + 32t2 = 480 + -480 + -64t + 64t + -32t2 + 32t2

Combine like terms: 480 + -480 = 0
-480 + 64t + 32t2 = 0 + -64t + 64t + -32t2 + 32t2
-480 + 64t + 32t2 = -64t + 64t + -32t2 + 32t2

Combine like terms: -64t + 64t = 0
-480 + 64t + 32t2 = 0 + -32t2 + 32t2
-480 + 64t + 32t2 = -32t2 + 32t2

Combine like terms: -32t2 + 32t2 = 0
-480 + 64t + 32t2 = 0

Factor out the Greatest Common Factor (GCF), '32'.
32(-15 + 2t + t2) = 0

Factor a trinomial.
32((-5 + -1t)(3 + -1t)) = 0

Ignore the factor 32.
Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 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 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-5, 3}