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

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

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

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

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

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

Combine like terms: -2t + -2t = -4t
(2 + -4t + 2t2) = 0

Solving
2 + -4t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2t + t2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {1, 1}