3t(4t-3)(3t-1)=0

Solution for 3t(4t-3)(3t-1)=0 equation:

Simplifying
3t(4t + -3)(3t + -1) = 0

Reorder the terms:
3t(-3 + 4t)(3t + -1) = 0

Reorder the terms:
3t(-3 + 4t)(-1 + 3t) = 0

Multiply (-3 + 4t) * (-1 + 3t)
3t(-3(-1 + 3t) + 4t * (-1 + 3t)) = 0
3t((-1 * -3 + 3t * -3) + 4t * (-1 + 3t)) = 0
3t((3 + -9t) + 4t * (-1 + 3t)) = 0
3t(3 + -9t + (-1 * 4t + 3t * 4t)) = 0
3t(3 + -9t + (-4t + 12t2)) = 0

Combine like terms: -9t + -4t = -13t
3t(3 + -13t + 12t2) = 0
(3 * 3t + -13t * 3t + 12t2 * 3t) = 0
(9t + -39t2 + 36t3) = 0

Solving
9t + -39t2 + 36t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(3 + -13t + 12t2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

Solving
1 + -3t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3t = 0 + -1
-3t = 0 + -1

Combine like terms: 0 + -1 = -1
-3t = -1

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Subproblem 3
Set the factor '(3 + -4t)' equal to zero and attempt to solve:

Simplifying
3 + -4t = 0

Solving
3 + -4t = 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 + -4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t = 0 + -3
-4t = 0 + -3

Combine like terms: 0 + -3 = -3
-4t = -3

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
Solution
t = {0, 0.3333333333, 0.75}