0=-t^2+2t+15

Solution for 0=-t^2+2t+15 equation:

Simplifying
0 = -1t2 + 2t + 15

Reorder the terms:
0 = 15 + 2t + -1t2

Solving
0 = 15 + 2t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -15 = -15
-15 + -2t + t2 = 15 + 2t + -1t2 + -15 + -2t + t2

Reorder the terms:
-15 + -2t + t2 = 15 + -15 + 2t + -2t + -1t2 + t2

Combine like terms: 15 + -15 = 0
-15 + -2t + t2 = 0 + 2t + -2t + -1t2 + t2
-15 + -2t + t2 = 2t + -2t + -1t2 + t2

Combine like terms: 2t + -2t = 0
-15 + -2t + t2 = 0 + -1t2 + t2
-15 + -2t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-15 + -2t + t2 = 0

Factor a trinomial.
(-3 + -1t)(5 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

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

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

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-3, 5}