12=8t-t^2

Solution for 12=8t-t^2 equation:

Simplifying
12 = 8t + -1t2

Solving
12 = 8t + -1t2

Solving for variable 't'.

Reorder the terms:
12 + -8t + t2 = 8t + -8t + -1t2 + t2

Combine like terms: 8t + -8t = 0
12 + -8t + t2 = 0 + -1t2 + t2
12 + -8t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
12 + -8t + t2 = 0

Factor a trinomial.
(2 + -1t)(6 + -1t) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

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

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

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {2, 6}