(t-9)(t+81)=0

Solution for (t-9)(t+81)=0 equation:

Simplifying
(t + -9)(t + 81) = 0

Reorder the terms:
(-9 + t)(t + 81) = 0

Reorder the terms:
(-9 + t)(81 + t) = 0

Multiply (-9 + t) * (81 + t)
(-9(81 + t) + t(81 + t)) = 0
((81 * -9 + t * -9) + t(81 + t)) = 0
((-729 + -9t) + t(81 + t)) = 0
(-729 + -9t + (81 * t + t * t)) = 0
(-729 + -9t + (81t + t2)) = 0

Combine like terms: -9t + 81t = 72t
(-729 + 72t + t2) = 0

Solving
-729 + 72t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-81 + -1t)(9 + -1t) = 0

Subproblem 1
Set the factor '(-81 + -1t)' equal to zero and attempt to solve:

Simplifying
-81 + -1t = 0

Solving
-81 + -1t = 0

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

Add '81' to each side of the equation.
-81 + 81 + -1t = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -1t = 0 + 81
-1t = 0 + 81

Combine like terms: 0 + 81 = 81
-1t = 81

Divide each side by '-1'.
t = -81

Simplifying
t = -81
Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve:

Simplifying
9 + -1t = 0

Solving
9 + -1t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1t = 0 + -9
-1t = 0 + -9

Combine like terms: 0 + -9 = -9
-1t = -9

Divide each side by '-1'.
t = 9

Simplifying
t = 9
Solution
t = {-81, 9}