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

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


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

Reorder the terms:
2(-4 + x) + -1(x + 2) = (x + 2)(x + -4)
(-4 * 2 + x * 2) + -1(x + 2) = (x + 2)(x + -4)
(-8 + 2x) + -1(x + 2) = (x + 2)(x + -4)

Reorder the terms:
-8 + 2x + -1(2 + x) = (x + 2)(x + -4)
-8 + 2x + (2 * -1 + x * -1) = (x + 2)(x + -4)
-8 + 2x + (-2 + -1x) = (x + 2)(x + -4)

Reorder the terms:
-8 + -2 + 2x + -1x = (x + 2)(x + -4)

Combine like terms: -8 + -2 = -10
-10 + 2x + -1x = (x + 2)(x + -4)

Combine like terms: 2x + -1x = 1x
-10 + 1x = (x + 2)(x + -4)

Reorder the terms:
-10 + 1x = (2 + x)(x + -4)

Reorder the terms:
-10 + 1x = (2 + x)(-4 + x)

Multiply (2 + x) * (-4 + x)
-10 + 1x = (2(-4 + x) + x(-4 + x))
-10 + 1x = ((-4 * 2 + x * 2) + x(-4 + x))
-10 + 1x = ((-8 + 2x) + x(-4 + x))
-10 + 1x = (-8 + 2x + (-4 * x + x * x))
-10 + 1x = (-8 + 2x + (-4x + x2))

Combine like terms: 2x + -4x = -2x
-10 + 1x = (-8 + -2x + x2)

Solving
-10 + 1x = -8 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-10 + 8 + 1x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: -10 + 8 = -2
-2 + 1x + 2x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Combine like terms: 1x + 2x = 3x
-2 + 3x + -1x2 = -8 + -2x + x2 + 8 + 2x + -1x2

Reorder the terms:
-2 + 3x + -1x2 = -8 + 8 + -2x + 2x + x2 + -1x2

Combine like terms: -8 + 8 = 0
-2 + 3x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-2 + 3x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-2 + 3x + -1x2 = 0 + x2 + -1x2
-2 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-2 + 3x + -1x2 = 0

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


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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2

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 = {2, 1}

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