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

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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}

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