72=72-6t-t^2

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

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

Add '-72' to each side of the equation.
72 + -72 = 72 + -6t + -72 + -1t2

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

Reorder the terms:
0 = 72 + -72 + -6t + -1t2

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

Solving
0 = -6t + -1t2

Solving for variable 't'.
Remove the zero:
6t + t2 = -6t + -1t2 + 6t + t2

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

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

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

Factor out the Greatest Common Factor (GCF), 't'.
t(6 + t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 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 + t = 0 + -6

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

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

Simplifying
t = -6
Solution
t = {0, -6}