(2x-5)(x-1)=2

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

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

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

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

Multiply (-5 + 2x) * (-1 + x)
(-5(-1 + x) + 2x * (-1 + x)) = 2
((-1 * -5 + x * -5) + 2x * (-1 + x)) = 2
((5 + -5x) + 2x * (-1 + x)) = 2
(5 + -5x + (-1 * 2x + x * 2x)) = 2
(5 + -5x + (-2x + 2x2)) = 2

Combine like terms: -5x + -2x = -7x
(5 + -7x + 2x2) = 2

Solving
5 + -7x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
5 + -2 + -7x + 2x2 = 2 + -2

Combine like terms: 5 + -2 = 3
3 + -7x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
3 + -7x + 2x2 = 0

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

Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}