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

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


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

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

Remove parenthesis around (3 + x)
3 + x = x2 + -2x + 5

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

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

Solving for variable 'x'.

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

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

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

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

Combine like terms: 5 + -5 = 0
-2 + 3x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-2 + 3x + -1x2 = -2x + 2x + x2 + -1x2

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

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

Factor a trinomial.
(-2 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2

Subproblem 2
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
Solution
x = {2, 1}

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