(2x-2)3x=12

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Solution for (2x-2)3x=12 equation:


Simplifying
(2x + -2) * 3x = 12

Reorder the terms:
(-2 + 2x) * 3x = 12

Reorder the terms for easier multiplication:
3x(-2 + 2x) = 12
(-2 * 3x + 2x * 3x) = 12
(-6x + 6x2) = 12

Solving
-6x + 6x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + -6x + 6x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -6x + 6x2 = 0

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

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

Ignore the factor 6.

Subproblem 1

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 2

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

Solution

x = {-1, 2}

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