(x^2-x)(x-5)=0

Solution for (x^2-x)(x-5)=0 equation:

Simplifying
(x2 + -1x)(x + -5) = 0

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

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

Multiply (-1x + x2) * (-5 + x)
(-1x * (-5 + x) + x2(-5 + x)) = 0
((-5 * -1x + x * -1x) + x2(-5 + x)) = 0
((5x + -1x2) + x2(-5 + x)) = 0
(5x + -1x2 + (-5 * x2 + x * x2)) = 0
(5x + -1x2 + (-5x2 + x3)) = 0

Combine like terms: -1x2 + -5x2 = -6x2
(5x + -6x2 + x3) = 0

Solving
5x + -6x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -6x + x2) = 0

Factor a trinomial.
x((1 + -1x)(5 + -1x)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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
Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 1, 5}