0=-t^2+4t+5

Solution for 0=-t^2+4t+5 equation:

Simplifying
0 = -1t2 + 4t + 5

Reorder the terms:
0 = 5 + 4t + -1t2

Solving
0 = 5 + 4t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + -4t + t2 = 5 + 4t + -1t2 + -5 + -4t + t2

Reorder the terms:
-5 + -4t + t2 = 5 + -5 + 4t + -4t + -1t2 + t2

Combine like terms: 5 + -5 = 0
-5 + -4t + t2 = 0 + 4t + -4t + -1t2 + t2
-5 + -4t + t2 = 4t + -4t + -1t2 + t2

Combine like terms: 4t + -4t = 0
-5 + -4t + t2 = 0 + -1t2 + t2
-5 + -4t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-5 + -4t + t2 = 0

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

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 '(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 = {-1, 5}