t^2-24t-81=0

Solution for t^2-24t-81=0 equation:

Simplifying
t2 + -24t + -81 = 0

Reorder the terms:
-81 + -24t + t2 = 0

Solving
-81 + -24t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-3 + -1t)(27 + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(27 + -1t)' equal to zero and attempt to solve:

Simplifying
27 + -1t = 0

Solving
27 + -1t = 0

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

Add '-27' to each side of the equation.
27 + -27 + -1t = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -1t = 0 + -27
-1t = 0 + -27

Combine like terms: 0 + -27 = -27
-1t = -27

Divide each side by '-1'.
t = 27

Simplifying
t = 27
Solution
t = {-3, 27}