0=5000-50t-t^2

Solution for 0=5000-50t-t^2 equation:

Simplifying
0 = 5000 + -50t + -1t2

Solving
0 = 5000 + -50t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -5000 = -5000
-5000 + 50t + t2 = 5000 + -50t + -1t2 + -5000 + 50t + t2

Reorder the terms:
-5000 + 50t + t2 = 5000 + -5000 + -50t + 50t + -1t2 + t2

Combine like terms: 5000 + -5000 = 0
-5000 + 50t + t2 = 0 + -50t + 50t + -1t2 + t2
-5000 + 50t + t2 = -50t + 50t + -1t2 + t2

Combine like terms: -50t + 50t = 0
-5000 + 50t + t2 = 0 + -1t2 + t2
-5000 + 50t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-5000 + 50t + t2 = 0

Factor a trinomial.
(-100 + -1t)(50 + -1t) = 0

Subproblem 1
Set the factor '(-100 + -1t)' equal to zero and attempt to solve:

Simplifying
-100 + -1t = 0

Solving
-100 + -1t = 0

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

Add '100' to each side of the equation.
-100 + 100 + -1t = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1t = 0 + 100
-1t = 0 + 100

Combine like terms: 0 + 100 = 100
-1t = 100

Divide each side by '-1'.
t = -100

Simplifying
t = -100
Subproblem 2
Set the factor '(50 + -1t)' equal to zero and attempt to solve:

Simplifying
50 + -1t = 0

Solving
50 + -1t = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1t = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1t = 0 + -50
-1t = 0 + -50

Combine like terms: 0 + -50 = -50
-1t = -50

Divide each side by '-1'.
t = 50

Simplifying
t = 50
Solution
t = {-100, 50}