x^2-3x+7=2x+1

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Solution for x^2-3x+7=2x+1 equation: 


Simplifying
x2 + -3x + 7 = 2x + 1

Reorder the terms:
7 + -3x + x2 = 2x + 1

Reorder the terms:
7 + -3x + x2 = 1 + 2x

Solving
7 + -3x + x2 = 1 + 2x

Solving for variable 'x'.

Reorder the terms:
7 + -1 + -3x + -2x + x2 = 1 + 2x + -1 + -2x

Combine like terms: 7 + -1 = 6
6 + -3x + -2x + x2 = 1 + 2x + -1 + -2x

Combine like terms: -3x + -2x = -5x
6 + -5x + x2 = 1 + 2x + -1 + -2x

Reorder the terms:
6 + -5x + x2 = 1 + -1 + 2x + -2x

Combine like terms: 1 + -1 = 0
6 + -5x + x2 = 0 + 2x + -2x
6 + -5x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -5x + x2 = 0

Factor a trinomial.
(2 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}

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