x^2+x+1=2x+3

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


Simplifying
x2 + x + 1 = 2x + 3

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

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

Solving
1 + x + x2 = 3 + 2x

Solving for variable 'x'.

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

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

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

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

Combine like terms: 3 + -3 = 0
-2 + -1x + x2 = 0 + 2x + -2x
-2 + -1x + x2 = 2x + -2x

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

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

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