50=-5t^2+15t+50

Solution for 50=-5t^2+15t+50 equation:

Simplifying
50 = -5t2 + 15t + 50

Reorder the terms:
50 = 50 + 15t + -5t2

Add '-50' to each side of the equation.
50 + -50 = 50 + 15t + -50 + -5t2

Combine like terms: 50 + -50 = 0
0 = 50 + 15t + -50 + -5t2

Reorder the terms:
0 = 50 + -50 + 15t + -5t2

Combine like terms: 50 + -50 = 0
0 = 0 + 15t + -5t2
0 = 15t + -5t2

Solving
0 = 15t + -5t2

Solving for variable 't'.
Remove the zero:
-15t + 5t2 = 15t + -5t2 + -15t + 5t2

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

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

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

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

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

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-3 + t)' equal to zero and attempt to solve:

Simplifying
-3 + t = 0

Solving
-3 + t = 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 + t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + t = 0 + 3
t = 0 + 3

Combine like terms: 0 + 3 = 3
t = 3

Simplifying
t = 3
Solution
t = {0, 3}