0=72-6t-t^2

Solution for 0=72-6t-t^2 equation:

Simplifying
0 = 72 + -6t + -1t2

Solving
0 = 72 + -6t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -72 = -72
-72 + 6t + t2 = 72 + -6t + -1t2 + -72 + 6t + t2

Reorder the terms:
-72 + 6t + t2 = 72 + -72 + -6t + 6t + -1t2 + t2

Combine like terms: 72 + -72 = 0
-72 + 6t + t2 = 0 + -6t + 6t + -1t2 + t2
-72 + 6t + t2 = -6t + 6t + -1t2 + t2

Combine like terms: -6t + 6t = 0
-72 + 6t + t2 = 0 + -1t2 + t2
-72 + 6t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-72 + 6t + t2 = 0

Factor a trinomial.
(-12 + -1t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-12 + -1t)' equal to zero and attempt to solve:

Simplifying
-12 + -1t = 0

Solving
-12 + -1t = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1t = 0 + 12

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

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

Divide each side by '-1'.
t = -12

Simplifying
t = -12
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 = {-12, 6}