x^2-2x=3x-4

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Solution for x^2-2x=3x-4 equation:


Simplifying
x2 + -2x = 3x + -4

Reorder the terms:
-2x + x2 = 3x + -4

Reorder the terms:
-2x + x2 = -4 + 3x

Solving
-2x + x2 = -4 + 3x

Solving for variable 'x'.

Reorder the terms:
4 + -2x + -3x + x2 = -4 + 3x + 4 + -3x

Combine like terms: -2x + -3x = -5x
4 + -5x + x2 = -4 + 3x + 4 + -3x

Reorder the terms:
4 + -5x + x2 = -4 + 4 + 3x + -3x

Combine like terms: -4 + 4 = 0
4 + -5x + x2 = 0 + 3x + -3x
4 + -5x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + -5x + x2 = 0

Factor a trinomial.
(1 + -1x)(4 + -1x) = 0

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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {1, 4}

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