0=12t-3t^2+36

Solution for 0=12t-3t^2+36 equation:

Simplifying
0 = 12t + -3t2 + 36

Reorder the terms:
0 = 36 + 12t + -3t2

Solving
0 = 36 + 12t + -3t2

Solving for variable 't'.

Combine like terms: 0 + -36 = -36
-36 + -12t + 3t2 = 36 + 12t + -3t2 + -36 + -12t + 3t2

Reorder the terms:
-36 + -12t + 3t2 = 36 + -36 + 12t + -12t + -3t2 + 3t2

Combine like terms: 36 + -36 = 0
-36 + -12t + 3t2 = 0 + 12t + -12t + -3t2 + 3t2
-36 + -12t + 3t2 = 12t + -12t + -3t2 + 3t2

Combine like terms: 12t + -12t = 0
-36 + -12t + 3t2 = 0 + -3t2 + 3t2
-36 + -12t + 3t2 = -3t2 + 3t2

Combine like terms: -3t2 + 3t2 = 0
-36 + -12t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -4t + t2) = 0

Factor a trinomial.
3((-2 + -1t)(6 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve:

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-2, 6}