2x-3(x-6)-x*x+36=x(x-6)

Solution for 2x-3(x-6)-x*x+36=x(x-6) equation:

Simplifying
2x + -3(x + -6) + -1x * x + 36 = x(x + -6)

Reorder the terms:
2x + -3(-6 + x) + -1x * x + 36 = x(x + -6)
2x + (-6 * -3 + x * -3) + -1x * x + 36 = x(x + -6)
2x + (18 + -3x) + -1x * x + 36 = x(x + -6)

Multiply x * x
2x + 18 + -3x + -1x2 + 36 = x(x + -6)

Reorder the terms:
18 + 36 + 2x + -3x + -1x2 = x(x + -6)

Combine like terms: 18 + 36 = 54
54 + 2x + -3x + -1x2 = x(x + -6)

Combine like terms: 2x + -3x = -1x
54 + -1x + -1x2 = x(x + -6)

Reorder the terms:
54 + -1x + -1x2 = x(-6 + x)
54 + -1x + -1x2 = (-6 * x + x * x)
54 + -1x + -1x2 = (-6x + x2)

Solving
54 + -1x + -1x2 = -6x + x2

Solving for variable 'x'.

Reorder the terms:
54 + -1x + 6x + -1x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: -1x + 6x = 5x
54 + 5x + -1x2 + -1x2 = -6x + x2 + 6x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
54 + 5x + -2x2 = -6x + x2 + 6x + -1x2

Reorder the terms:
54 + 5x + -2x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
54 + 5x + -2x2 = 0 + x2 + -1x2
54 + 5x + -2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
54 + 5x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-27 + -2.5x + x2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2.5x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -2.5x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2.5x + x2 = 0 + 27
-2.5x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2.5x + x2 = 27

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 27 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 27 + 1.5625

Combine like terms: 27 + 1.5625 = 28.5625
1.5625 + -2.5x + x2 = 28.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(x + -1.25) equal to 5.344389582 and -5.344389582.

Subproblem 1
x + -1.25 = 5.344389582

Simplifying
x + -1.25 = 5.344389582

Reorder the terms:
-1.25 + x = 5.344389582

Solving
-1.25 + x = 5.344389582

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 5.344389582 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 5.344389582 + 1.25
x = 5.344389582 + 1.25

Combine like terms: 5.344389582 + 1.25 = 6.594389582
x = 6.594389582

Simplifying
x = 6.594389582

Subproblem 2
x + -1.25 = -5.344389582

Simplifying
x + -1.25 = -5.344389582

Reorder the terms:
-1.25 + x = -5.344389582

Solving
-1.25 + x = -5.344389582

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -5.344389582 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -5.344389582 + 1.25
x = -5.344389582 + 1.25

Combine like terms: -5.344389582 + 1.25 = -4.094389582
x = -4.094389582

Simplifying
x = -4.094389582

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.594389582, -4.094389582}