x-1=x^2-6x+9

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Solution for x-1=x^2-6x+9 equation: 


Simplifying
x + -1 = x2 + -6x + 9

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

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

Solving
-1 + x = 9 + -6x + x2

Solving for variable 'x'.

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

Combine like terms: -1 + -9 = -10
-10 + x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: x + 6x = 7x
-10 + 7x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
-10 + 7x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-10 + 7x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-10 + 7x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-10 + 7x + -1x2 = 0 + x2 + -1x2
-10 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 7x + -1x2 = 0

Factor a trinomial.
(-5 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5

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 = {5, 2}

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