x^2-3x+6=x+2

Solution for x^2-3x+6=x+2 equation:

Simplifying
x2 + -3x + 6 = x + 2

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

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

Solving
6 + -3x + x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
6 + -2 + -3x + -1x + x2 = 2 + x + -2 + -1x

Combine like terms: 6 + -2 = 4
4 + -3x + -1x + x2 = 2 + x + -2 + -1x

Combine like terms: -3x + -1x = -4x
4 + -4x + x2 = 2 + x + -2 + -1x

Reorder the terms:
4 + -4x + x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
4 + -4x + x2 = 0 + x + -1x
4 + -4x + x2 = x + -1x

Combine like terms: x + -1x = 0
4 + -4x + x2 = 0

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