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

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


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

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

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

Solving for variable 'x'.

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

Combine like terms: -8x + -4x = -12x
-12x + 2x2 + x2 = 4x + -1x2 + -4x + x2

Combine like terms: 2x2 + x2 = 3x2
-12x + 3x2 = 4x + -1x2 + -4x + x2

Reorder the terms:
-12x + 3x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
-12x + 3x2 = 0 + -1x2 + x2
-12x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Simplifying x = 4

Solution

x = {0, 4}

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