(2t-5)(t-1)=2

Solution for (2t-5)(t-1)=2 equation:

Simplifying
(2t + -5)(t + -1) = 2

Reorder the terms:
(-5 + 2t)(t + -1) = 2

Reorder the terms:
(-5 + 2t)(-1 + t) = 2

Multiply (-5 + 2t) * (-1 + t)
(-5(-1 + t) + 2t * (-1 + t)) = 2
((-1 * -5 + t * -5) + 2t * (-1 + t)) = 2
((5 + -5t) + 2t * (-1 + t)) = 2
(5 + -5t + (-1 * 2t + t * 2t)) = 2
(5 + -5t + (-2t + 2t2)) = 2

Combine like terms: -5t + -2t = -7t
(5 + -7t + 2t2) = 2

Solving
5 + -7t + 2t2 = 2

Solving for variable 't'.

Reorder the terms:
5 + -2 + -7t + 2t2 = 2 + -2

Combine like terms: 5 + -2 = 3
3 + -7t + 2t2 = 2 + -2

Combine like terms: 2 + -2 = 0
3 + -7t + 2t2 = 0

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

Subproblem 1
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 2
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 = {0.5, 3}