0=t^2-24t-180

Solution for 0=t^2-24t-180 equation:

Simplifying
0 = t2 + -24t + -180

Reorder the terms:
0 = -180 + -24t + t2

Solving
0 = -180 + -24t + t2

Solving for variable 't'.

Combine like terms: 0 + 180 = 180
180 + 24t + -1t2 = -180 + -24t + t2 + 180 + 24t + -1t2

Reorder the terms:
180 + 24t + -1t2 = -180 + 180 + -24t + 24t + t2 + -1t2

Combine like terms: -180 + 180 = 0
180 + 24t + -1t2 = 0 + -24t + 24t + t2 + -1t2
180 + 24t + -1t2 = -24t + 24t + t2 + -1t2

Combine like terms: -24t + 24t = 0
180 + 24t + -1t2 = 0 + t2 + -1t2
180 + 24t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
180 + 24t + -1t2 = 0

Factor a trinomial.
(30 + -1t)(6 + t) = 0

Subproblem 1
Set the factor '(30 + -1t)' equal to zero and attempt to solve:

Simplifying
30 + -1t = 0

Solving
30 + -1t = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1t = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1t = 0 + -30
-1t = 0 + -30

Combine like terms: 0 + -30 = -30
-1t = -30

Divide each side by '-1'.
t = 30

Simplifying
t = 30
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 = {30, -6}