(t-9)(t+36)=0

Solution for (t-9)(t+36)=0 equation:

Simplifying
(t + -9)(t + 36) = 0

Reorder the terms:
(-9 + t)(t + 36) = 0

Reorder the terms:
(-9 + t)(36 + t) = 0

Multiply (-9 + t) * (36 + t)
(-9(36 + t) + t(36 + t)) = 0
((36 * -9 + t * -9) + t(36 + t)) = 0
((-324 + -9t) + t(36 + t)) = 0
(-324 + -9t + (36 * t + t * t)) = 0
(-324 + -9t + (36t + t2)) = 0

Combine like terms: -9t + 36t = 27t
(-324 + 27t + t2) = 0

Solving
-324 + 27t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-36 + -1t)(9 + -1t) = 0

Subproblem 1
Set the factor '(-36 + -1t)' equal to zero and attempt to solve:

Simplifying
-36 + -1t = 0

Solving
-36 + -1t = 0

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

Add '36' to each side of the equation.
-36 + 36 + -1t = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1t = 0 + 36
-1t = 0 + 36

Combine like terms: 0 + 36 = 36
-1t = 36

Divide each side by '-1'.
t = -36

Simplifying
t = -36
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 = {-36, 9}