0=3t^2-24t+36

Solution for 0=3t^2-24t+36 equation:

Simplifying
0 = 3t2 + -24t + 36

Reorder the terms:
0 = 36 + -24t + 3t2

Solving
0 = 36 + -24t + 3t2

Solving for variable 't'.

Combine like terms: 0 + -36 = -36
-36 + 24t + -3t2 = 36 + -24t + 3t2 + -36 + 24t + -3t2

Reorder the terms:
-36 + 24t + -3t2 = 36 + -36 + -24t + 24t + 3t2 + -3t2

Combine like terms: 36 + -36 = 0
-36 + 24t + -3t2 = 0 + -24t + 24t + 3t2 + -3t2
-36 + 24t + -3t2 = -24t + 24t + 3t2 + -3t2

Combine like terms: -24t + 24t = 0
-36 + 24t + -3t2 = 0 + 3t2 + -3t2
-36 + 24t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-36 + 24t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8t + -1t2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve:

Simplifying
-6 + t = 0

Solving
-6 + t = 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 + t = 0 + 6

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

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

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