(t-6)(3t-6)=0

Solution for (t-6)(3t-6)=0 equation:

Simplifying
(t + -6)(3t + -6) = 0

Reorder the terms:
(-6 + t)(3t + -6) = 0

Reorder the terms:
(-6 + t)(-6 + 3t) = 0

Multiply (-6 + t) * (-6 + 3t)
(-6(-6 + 3t) + t(-6 + 3t)) = 0
((-6 * -6 + 3t * -6) + t(-6 + 3t)) = 0
((36 + -18t) + t(-6 + 3t)) = 0
(36 + -18t + (-6 * t + 3t * t)) = 0
(36 + -18t + (-6t + 3t2)) = 0

Combine like terms: -18t + -6t = -24t
(36 + -24t + 3t2) = 0

Solving
36 + -24t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -8t + 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}