50=65+10t-5t^2

Solution for 50=65+10t-5t^2 equation:

Simplifying
50 = 65 + 10t + -5t2

Solving
50 = 65 + 10t + -5t2

Solving for variable 't'.

Combine like terms: 50 + -65 = -15
-15 + -10t + 5t2 = 65 + 10t + -5t2 + -65 + -10t + 5t2

Reorder the terms:
-15 + -10t + 5t2 = 65 + -65 + 10t + -10t + -5t2 + 5t2

Combine like terms: 65 + -65 = 0
-15 + -10t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2
-15 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2

Combine like terms: 10t + -10t = 0
-15 + -10t + 5t2 = 0 + -5t2 + 5t2
-15 + -10t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-15 + -10t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2t + t2) = 0

Factor a trinomial.
5((-1 + -1t)(3 + -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 '(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 = {-1, 3}