6x-2=x^2-6x+9

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Solution for 6x-2=x^2-6x+9 equation: 


Simplifying
6x + -2 = x2 + -6x + 9

Reorder the terms:
-2 + 6x = x2 + -6x + 9

Reorder the terms:
-2 + 6x = 9 + -6x + x2

Solving
-2 + 6x = 9 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + -9 + 6x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: -2 + -9 = -11
-11 + 6x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 6x + 6x = 12x
-11 + 12x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
-11 + 12x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-11 + 12x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-11 + 12x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-11 + 12x + -1x2 = 0 + x2 + -1x2
-11 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + 12x + -1x2 = 0

Factor a trinomial.
(-11 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Simplifying
x = 11

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 = {11, 1}

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