t(2t-1)(t-3)=0

Solution for t(2t-1)(t-3)=0 equation:

Simplifying
t(2t + -1)(t + -3) = 0

Reorder the terms:
t(-1 + 2t)(t + -3) = 0

Reorder the terms:
t(-1 + 2t)(-3 + t) = 0

Multiply (-1 + 2t) * (-3 + t)
t(-1(-3 + t) + 2t * (-3 + t)) = 0
t((-3 * -1 + t * -1) + 2t * (-3 + t)) = 0
t((3 + -1t) + 2t * (-3 + t)) = 0
t(3 + -1t + (-3 * 2t + t * 2t)) = 0
t(3 + -1t + (-6t + 2t2)) = 0

Combine like terms: -1t + -6t = -7t
t(3 + -7t + 2t2) = 0
(3 * t + -7t * t + 2t2 * t) = 0
(3t + -7t2 + 2t3) = 0

Solving
3t + -7t2 + 2t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(3 + -7t + 2t2) = 0

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

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 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Subproblem 3
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {0, 0.5, 3}