3(x-2)+(x-2)x=2x

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


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

Reorder the terms:
3(-2 + x) + (x + -2) * x = 2x
(-2 * 3 + x * 3) + (x + -2) * x = 2x
(-6 + 3x) + (x + -2) * x = 2x

Reorder the terms:
-6 + 3x + (-2 + x) * x = 2x

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

Combine like terms: 3x + -2x = 1x
-6 + 1x + x2 = 2x

Solving
-6 + 1x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 1x + -2x + x2 = 2x + -2x

Combine like terms: 1x + -2x = -1x
-6 + -1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-6 + -1x + x2 = 0

Factor a trinomial.
(-2 + -1x)(3 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2, 3}

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