2x^2-6x+6=18-2x+x^2

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Solution for 2x^2-6x+6=18-2x+x^2 equation: 


Simplifying
2x2 + -6x + 6 = 18 + -2x + x2

Reorder the terms:
6 + -6x + 2x2 = 18 + -2x + x2

Solving
6 + -6x + 2x2 = 18 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
6 + -18 + -6x + 2x + 2x2 + -1x2 = 18 + -2x + x2 + -18 + 2x + -1x2

Combine like terms: 6 + -18 = -12
-12 + -6x + 2x + 2x2 + -1x2 = 18 + -2x + x2 + -18 + 2x + -1x2

Combine like terms: -6x + 2x = -4x
-12 + -4x + 2x2 + -1x2 = 18 + -2x + x2 + -18 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-12 + -4x + 1x2 = 18 + -2x + x2 + -18 + 2x + -1x2

Reorder the terms:
-12 + -4x + 1x2 = 18 + -18 + -2x + 2x + x2 + -1x2

Combine like terms: 18 + -18 = 0
-12 + -4x + 1x2 = 0 + -2x + 2x + x2 + -1x2
-12 + -4x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-12 + -4x + 1x2 = 0 + x2 + -1x2
-12 + -4x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + -4x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}

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