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

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

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

Reorder the terms:
x(-1 + x) + -1(5)(x + -2) = 2
(-1 * x + x * x) + -1(5)(x + -2) = 2
(-1x + x2) + -1(5)(x + -2) = 2

Reorder the terms:
-1x + x2 + -1 * 5(-2 + x) = 2

Multiply -1 * 5
-1x + x2 + -5(-2 + x) = 2
-1x + x2 + (-2 * -5 + x * -5) = 2
-1x + x2 + (10 + -5x) = 2

Reorder the terms:
10 + -1x + -5x + x2 = 2

Combine like terms: -1x + -5x = -6x
10 + -6x + x2 = 2

Solving
10 + -6x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
10 + -2 + -6x + x2 = 2 + -2

Combine like terms: 10 + -2 = 8
8 + -6x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {2, 4}