2x^2-4x=4-2x

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


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

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

Solving
-4x + 2x2 = 4 + -2x

Solving for variable 'x'.

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

Combine like terms: -4x + 2x = -2x
-4 + -2x + 2x2 = 4 + -2x + -4 + 2x

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

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

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

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

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

Ignore the factor 2.

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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