2x-(x+2)=(4-x)(x-2)

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Solution for 2x-(x+2)=(4-x)(x-2) equation: 


Simplifying
2x + -1(x + 2) = (4 + -1x)(x + -2)

Reorder the terms:
2x + -1(2 + x) = (4 + -1x)(x + -2)
2x + (2 * -1 + x * -1) = (4 + -1x)(x + -2)
2x + (-2 + -1x) = (4 + -1x)(x + -2)

Reorder the terms:
-2 + 2x + -1x = (4 + -1x)(x + -2)

Combine like terms: 2x + -1x = 1x
-2 + 1x = (4 + -1x)(x + -2)

Reorder the terms:
-2 + 1x = (4 + -1x)(-2 + x)

Multiply (4 + -1x) * (-2 + x)
-2 + 1x = (4(-2 + x) + -1x * (-2 + x))
-2 + 1x = ((-2 * 4 + x * 4) + -1x * (-2 + x))
-2 + 1x = ((-8 + 4x) + -1x * (-2 + x))
-2 + 1x = (-8 + 4x + (-2 * -1x + x * -1x))
-2 + 1x = (-8 + 4x + (2x + -1x2))

Combine like terms: 4x + 2x = 6x
-2 + 1x = (-8 + 6x + -1x2)

Solving
-2 + 1x = -8 + 6x + -1x2

Solving for variable 'x'.

Reorder the terms:
-2 + 8 + 1x + -6x + x2 = -8 + 6x + -1x2 + 8 + -6x + x2

Combine like terms: -2 + 8 = 6
6 + 1x + -6x + x2 = -8 + 6x + -1x2 + 8 + -6x + x2

Combine like terms: 1x + -6x = -5x
6 + -5x + x2 = -8 + 6x + -1x2 + 8 + -6x + x2

Reorder the terms:
6 + -5x + x2 = -8 + 8 + 6x + -6x + -1x2 + x2

Combine like terms: -8 + 8 = 0
6 + -5x + x2 = 0 + 6x + -6x + -1x2 + x2
6 + -5x + x2 = 6x + -6x + -1x2 + x2

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

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