8-4x=2x+4-x^2-2x

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Solution for 8-4x=2x+4-x^2-2x equation: 


Simplifying
8 + -4x = 2x + 4 + -1x2 + -2x

Reorder the terms:
8 + -4x = 4 + 2x + -2x + -1x2

Combine like terms: 2x + -2x = 0
8 + -4x = 4 + 0 + -1x2
8 + -4x = 4 + -1x2

Solving
8 + -4x = 4 + -1x2

Solving for variable 'x'.

Reorder the terms:
8 + -4 + -4x + x2 = 4 + -1x2 + -4 + x2

Combine like terms: 8 + -4 = 4
4 + -4x + x2 = 4 + -1x2 + -4 + x2

Reorder the terms:
4 + -4x + x2 = 4 + -4 + -1x2 + x2

Combine like terms: 4 + -4 = 0
4 + -4x + x2 = 0 + -1x2 + x2
4 + -4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
4 + -4x + x2 = 0

Factor a trinomial.
(2 + -1x)(2 + -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 '(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 = {2, 2}

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