50=55t-5t^2

Solution for 50=55t-5t^2 equation:

Simplifying
50 = 55t + -5t2

Solving
50 = 55t + -5t2

Solving for variable 't'.

Reorder the terms:
50 + -55t + 5t2 = 55t + -55t + -5t2 + 5t2

Combine like terms: 55t + -55t = 0
50 + -55t + 5t2 = 0 + -5t2 + 5t2
50 + -55t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
50 + -55t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + -11t + t2) = 0

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

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
Subproblem 2
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
Solution
t = {1, 10}