(6-x)(x-1)(x*2-2x+2)=0

Solution for (6-x)(x-1)(x*2-2x+2)=0 equation:

Simplifying
(6 + -1x)(x + -1)(x * 2 + -2x + 2) = 0

Reorder the terms:
(6 + -1x)(-1 + x)(x * 2 + -2x + 2) = 0

Reorder the terms for easier multiplication:
(6 + -1x)(-1 + x)(2x + -2x + 2) = 0

Reorder the terms:
(6 + -1x)(-1 + x)(2 + 2x + -2x) = 0

Combine like terms: 2x + -2x = 0
(6 + -1x)(-1 + x)(2 + 0) = 0
(6 + -1x)(-1 + x)(2) = 0

Reorder the terms for easier multiplication:
2(6 + -1x)(-1 + x) = 0

Multiply (6 + -1x) * (-1 + x)
2(6(-1 + x) + -1x * (-1 + x)) = 0
2((-1 * 6 + x * 6) + -1x * (-1 + x)) = 0
2((-6 + 6x) + -1x * (-1 + x)) = 0
2(-6 + 6x + (-1 * -1x + x * -1x)) = 0
2(-6 + 6x + (1x + -1x2)) = 0

Combine like terms: 6x + 1x = 7x
2(-6 + 7x + -1x2) = 0
(-6 * 2 + 7x * 2 + -1x2 * 2) = 0
(-12 + 14x + -2x2) = 0

Solving
-12 + 14x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7x + -1x2) = 0

Factor a trinomial.
2((-6 + x)(1 + -1x)) = 0

Ignore the factor 2.
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}