0=-t^2+3t+4

Solution for 0=-t^2+3t+4 equation:

Simplifying
0 = -1t2 + 3t + 4

Reorder the terms:
0 = 4 + 3t + -1t2

Solving
0 = 4 + 3t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -4 = -4
-4 + -3t + t2 = 4 + 3t + -1t2 + -4 + -3t + t2

Reorder the terms:
-4 + -3t + t2 = 4 + -4 + 3t + -3t + -1t2 + t2

Combine like terms: 4 + -4 = 0
-4 + -3t + t2 = 0 + 3t + -3t + -1t2 + t2
-4 + -3t + t2 = 3t + -3t + -1t2 + t2

Combine like terms: 3t + -3t = 0
-4 + -3t + t2 = 0 + -1t2 + t2
-4 + -3t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-4 + -3t + t2 = 0

Factor a trinomial.
(-1 + -1t)(4 + -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 '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1, 4}