0=1000-120t-16t^2

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Solution for 0=1000-120t-16t^2 equation: 


Simplifying
0 = 1000 + -120t + -16t2

Solving
0 = 1000 + -120t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -1000 = -1000
-1000 + 120t + 16t2 = 1000 + -120t + -16t2 + -1000 + 120t + 16t2

Reorder the terms:
-1000 + 120t + 16t2 = 1000 + -1000 + -120t + 120t + -16t2 + 16t2

Combine like terms: 1000 + -1000 = 0
-1000 + 120t + 16t2 = 0 + -120t + 120t + -16t2 + 16t2
-1000 + 120t + 16t2 = -120t + 120t + -16t2 + 16t2

Combine like terms: -120t + 120t = 0
-1000 + 120t + 16t2 = 0 + -16t2 + 16t2
-1000 + 120t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-1000 + 120t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-125 + 15t + 2t2) = 0

Factor a trinomial.
8((-25 + -2t)(5 + -1t)) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-25 + -2t)' equal to zero and attempt to solve:

Simplifying
-25 + -2t = 0

Solving
-25 + -2t = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2t = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2t = 0 + 25
-2t = 0 + 25

Combine like terms: 0 + 25 = 25
-2t = 25

Divide each side by '-2'.
t = -12.5

Simplifying
t = -12.5

Subproblem 2
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
Solution
t = {-12.5, 5}

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