x^2=6x-9

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

Simplifying
x2 = 6x + -9

Reorder the terms:
x2 = -9 + 6x

Solving
x2 = -9 + 6x

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(3 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}