0=-t^2+2t+3

Solution for 0=-t^2+2t+3 equation:

Simplifying
0 = -1t2 + 2t + 3

Reorder the terms:
0 = 3 + 2t + -1t2

Solving
0 = 3 + 2t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -3 = -3
-3 + -2t + t2 = 3 + 2t + -1t2 + -3 + -2t + t2

Reorder the terms:
-3 + -2t + t2 = 3 + -3 + 2t + -2t + -1t2 + t2

Combine like terms: 3 + -3 = 0
-3 + -2t + t2 = 0 + 2t + -2t + -1t2 + t2
-3 + -2t + t2 = 2t + -2t + -1t2 + t2

Combine like terms: 2t + -2t = 0
-3 + -2t + t2 = 0 + -1t2 + t2
-3 + -2t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-3 + -2t + t2 = 0

Factor a trinomial.
(-1 + -1t)(3 + -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 '(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}