(x-1)-(x-1)(x-5)=0

Solution for (x-1)-(x-1)(x-5)=0 equation:

Simplifying
(x + -1) + -1(x + -1)(x + -5) = 0

Reorder the terms:
(-1 + x) + -1(x + -1)(x + -5) = 0

Remove parenthesis around (-1 + x)
-1 + x + -1(x + -1)(x + -5) = 0

Reorder the terms:
-1 + x + -1(-1 + x)(x + -5) = 0

Reorder the terms:
-1 + x + -1(-1 + x)(-5 + x) = 0

Multiply (-1 + x) * (-5 + x)
-1 + x + -1(-1(-5 + x) + x(-5 + x)) = 0
-1 + x + -1((-5 * -1 + x * -1) + x(-5 + x)) = 0
-1 + x + -1((5 + -1x) + x(-5 + x)) = 0
-1 + x + -1(5 + -1x + (-5 * x + x * x)) = 0
-1 + x + -1(5 + -1x + (-5x + x2)) = 0

Combine like terms: -1x + -5x = -6x
-1 + x + -1(5 + -6x + x2) = 0
-1 + x + (5 * -1 + -6x * -1 + x2 * -1) = 0
-1 + x + (-5 + 6x + -1x2) = 0

Reorder the terms:
-1 + -5 + x + 6x + -1x2 = 0

Combine like terms: -1 + -5 = -6
-6 + x + 6x + -1x2 = 0

Combine like terms: x + 6x = 7x
-6 + 7x + -1x2 = 0

Solving
-6 + 7x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {6, 1}