0=t^2-9t-36

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

Simplifying
0 = t2 + -9t + -36

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

Solving
0 = -36 + -9t + t2

Solving for variable 't'.

Combine like terms: 0 + 36 = 36
36 + 9t + -1t2 = -36 + -9t + t2 + 36 + 9t + -1t2

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

Combine like terms: -36 + 36 = 0
36 + 9t + -1t2 = 0 + -9t + 9t + t2 + -1t2
36 + 9t + -1t2 = -9t + 9t + t2 + -1t2

Combine like terms: -9t + 9t = 0
36 + 9t + -1t2 = 0 + t2 + -1t2
36 + 9t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
36 + 9t + -1t2 = 0

Factor a trinomial.
(12 + -1t)(3 + t) = 0

Subproblem 1
Set the factor '(12 + -1t)' equal to zero and attempt to solve:

Simplifying
12 + -1t = 0

Solving
12 + -1t = 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 + -1t = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1t = 0 + -12
-1t = 0 + -12

Combine like terms: 0 + -12 = -12
-1t = -12

Divide each side by '-1'.
t = 12

Simplifying
t = 12
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

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