(3t-12)(t-8)=0

Solution for (3t-12)(t-8)=0 equation:

Simplifying
(3t + -12)(t + -8) = 0

Reorder the terms:
(-12 + 3t)(t + -8) = 0

Reorder the terms:
(-12 + 3t)(-8 + t) = 0

Multiply (-12 + 3t) * (-8 + t)
(-12(-8 + t) + 3t * (-8 + t)) = 0
((-8 * -12 + t * -12) + 3t * (-8 + t)) = 0
((96 + -12t) + 3t * (-8 + t)) = 0
(96 + -12t + (-8 * 3t + t * 3t)) = 0
(96 + -12t + (-24t + 3t2)) = 0

Combine like terms: -12t + -24t = -36t
(96 + -36t + 3t2) = 0

Solving
96 + -36t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + -12t + t2) = 0

Factor a trinomial.
3((4 + -1t)(8 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Solution
t = {4, 8}