x^2-4x+5=2x-3

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Solution for x^2-4x+5=2x-3 equation: 


Simplifying
x2 + -4x + 5 = 2x + -3

Reorder the terms:
5 + -4x + x2 = 2x + -3

Reorder the terms:
5 + -4x + x2 = -3 + 2x

Solving
5 + -4x + x2 = -3 + 2x

Solving for variable 'x'.

Reorder the terms:
5 + 3 + -4x + -2x + x2 = -3 + 2x + 3 + -2x

Combine like terms: 5 + 3 = 8
8 + -4x + -2x + x2 = -3 + 2x + 3 + -2x

Combine like terms: -4x + -2x = -6x
8 + -6x + x2 = -3 + 2x + 3 + -2x

Reorder the terms:
8 + -6x + x2 = -3 + 3 + 2x + -2x

Combine like terms: -3 + 3 = 0
8 + -6x + x2 = 0 + 2x + -2x
8 + -6x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
8 + -6x + x2 = 0

Factor a trinomial.
(2 + -1x)(4 + -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 '(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 = {2, 4}

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