3=4t-t^2

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

Simplifying
3 = 4t + -1t2

Solving
3 = 4t + -1t2

Solving for variable 't'.

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

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

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