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

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

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

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

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

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

Combine like terms: -1t + -3t = -4t
(1 + -4t + 3t2) = 0

Solving
1 + -4t + 3t2 = 0

Solving for variable 't'.

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

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

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Solution
t = {0.3333333333, 1}