2x^2-5x=x^2+3x

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Solution for 2x^2-5x=x^2+3x equation:


Simplifying
2x2 + -5x = x2 + 3x

Reorder the terms:
-5x + 2x2 = x2 + 3x

Reorder the terms:
-5x + 2x2 = 3x + x2

Solving
-5x + 2x2 = 3x + x2

Solving for variable 'x'.

Reorder the terms:
-5x + -3x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

Combine like terms: -5x + -3x = -8x
-8x + 2x2 + -1x2 = 3x + x2 + -3x + -1x2

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + x) = 0

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 '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8

Solution

x = {0, 8}

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