5t-t^2=-50

Solution for 5t-t^2=-50 equation:

Simplifying
5t + -1t2 = -50

Solving
5t + -1t2 = -50

Solving for variable 't'.

Reorder the terms:
50 + 5t + -1t2 = -50 + 50

Combine like terms: -50 + 50 = 0
50 + 5t + -1t2 = 0

Factor a trinomial.
(10 + -1t)(5 + t) = 0

Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Subproblem 2
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

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

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

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

Simplifying
t = -5
Solution
t = {10, -5}