(x-6)(x-3)=x-6+x-3

Solution for (x-6)(x-3)=x-6+x-3 equation:

Simplifying
(x + -6)(x + -3) = x + -6 + x + -3

Reorder the terms:
(-6 + x)(x + -3) = x + -6 + x + -3

Reorder the terms:
(-6 + x)(-3 + x) = x + -6 + x + -3

Multiply (-6 + x) * (-3 + x)
(-6(-3 + x) + x(-3 + x)) = x + -6 + x + -3
((-3 * -6 + x * -6) + x(-3 + x)) = x + -6 + x + -3
((18 + -6x) + x(-3 + x)) = x + -6 + x + -3
(18 + -6x + (-3 * x + x * x)) = x + -6 + x + -3
(18 + -6x + (-3x + x2)) = x + -6 + x + -3

Combine like terms: -6x + -3x = -9x
(18 + -9x + x2) = x + -6 + x + -3

Reorder the terms:
18 + -9x + x2 = -6 + -3 + x + x

Combine like terms: -6 + -3 = -9
18 + -9x + x2 = -9 + x + x

Combine like terms: x + x = 2x
18 + -9x + x2 = -9 + 2x

Solving
18 + -9x + x2 = -9 + 2x

Solving for variable 'x'.

Reorder the terms:
18 + 9 + -9x + -2x + x2 = -9 + 2x + 9 + -2x

Combine like terms: 18 + 9 = 27
27 + -9x + -2x + x2 = -9 + 2x + 9 + -2x

Combine like terms: -9x + -2x = -11x
27 + -11x + x2 = -9 + 2x + 9 + -2x

Reorder the terms:
27 + -11x + x2 = -9 + 9 + 2x + -2x

Combine like terms: -9 + 9 = 0
27 + -11x + x2 = 0 + 2x + -2x
27 + -11x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
27 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -11x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -11x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -11x + x2 = 0 + -27
-11x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-11x + x2 = -27

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -27 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -27 + 30.25

Combine like terms: -27 + 30.25 = 3.25
30.25 + -11x + x2 = 3.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + -5.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + -5.5 = 1.802775638

Simplifying
x + -5.5 = 1.802775638

Reorder the terms:
-5.5 + x = 1.802775638

Solving
-5.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 1.802775638 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 1.802775638 + 5.5
x = 1.802775638 + 5.5

Combine like terms: 1.802775638 + 5.5 = 7.302775638
x = 7.302775638

Simplifying
x = 7.302775638

Subproblem 2
x + -5.5 = -1.802775638

Simplifying
x + -5.5 = -1.802775638

Reorder the terms:
-5.5 + x = -1.802775638

Solving
-5.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -1.802775638 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -1.802775638 + 5.5
x = -1.802775638 + 5.5

Combine like terms: -1.802775638 + 5.5 = 3.697224362
x = 3.697224362

Simplifying
x = 3.697224362

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.302775638, 3.697224362}