x^2-9x=x-9

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

Simplifying
x2 + -9x = x + -9

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

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

Solving
-9x + x2 = -9 + x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(9 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {1, 9}