-t^2-9t+36=0

Solution for -t^2-9t+36=0 equation:

Simplifying
-1t2 + -9t + 36 = 0

Reorder the terms:
36 + -9t + -1t2 = 0

Solving
36 + -9t + -1t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -1t)(12 + t) = 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 '(12 + t)' equal to zero and attempt to solve:

Simplifying
12 + t = 0

Solving
12 + t = 0

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

Add '-12' to each side of the equation.
12 + -12 + t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + t = 0 + -12
t = 0 + -12

Combine like terms: 0 + -12 = -12
t = -12

Simplifying
t = -12
Solution
t = {3, -12}