(2x-3)2-3x^2=(x-6)2

Solution for (2x-3)2-3x^2=(x-6)2 equation:

Simplifying
(2x + -3) * 2 + -3x2 = (x + -6) * 2

Reorder the terms:
(-3 + 2x) * 2 + -3x2 = (x + -6) * 2

Reorder the terms for easier multiplication:
2(-3 + 2x) + -3x2 = (x + -6) * 2
(-3 * 2 + 2x * 2) + -3x2 = (x + -6) * 2
(-6 + 4x) + -3x2 = (x + -6) * 2

Reorder the terms:
-6 + 4x + -3x2 = (-6 + x) * 2

Reorder the terms for easier multiplication:
-6 + 4x + -3x2 = 2(-6 + x)
-6 + 4x + -3x2 = (-6 * 2 + x * 2)
-6 + 4x + -3x2 = (-12 + 2x)

Solving
-6 + 4x + -3x2 = -12 + 2x

Solving for variable 'x'.

Reorder the terms:
-6 + 12 + 4x + -2x + -3x2 = -12 + 2x + 12 + -2x

Combine like terms: -6 + 12 = 6
6 + 4x + -2x + -3x2 = -12 + 2x + 12 + -2x

Combine like terms: 4x + -2x = 2x
6 + 2x + -3x2 = -12 + 2x + 12 + -2x

Reorder the terms:
6 + 2x + -3x2 = -12 + 12 + 2x + -2x

Combine like terms: -12 + 12 = 0
6 + 2x + -3x2 = 0 + 2x + -2x
6 + 2x + -3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 2x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-2 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.6666666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.6666666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.6666666667x + x2 = 0 + 2
-0.6666666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.6666666667x + x2 = 2

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 2 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 2 + 0.1111111112

Combine like terms: 2 + 0.1111111112 = 2.1111111112
0.1111111112 + -0.6666666667x + x2 = 2.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 2.1111111112

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1
x + -0.3333333334 = 1.452966315

Simplifying
x + -0.3333333334 = 1.452966315

Reorder the terms:
-0.3333333334 + x = 1.452966315

Solving
-0.3333333334 + x = 1.452966315

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.452966315 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.452966315 + 0.3333333334
x = 1.452966315 + 0.3333333334

Combine like terms: 1.452966315 + 0.3333333334 = 1.7862996484
x = 1.7862996484

Simplifying
x = 1.7862996484

Subproblem 2
x + -0.3333333334 = -1.452966315

Simplifying
x + -0.3333333334 = -1.452966315

Reorder the terms:
-0.3333333334 + x = -1.452966315

Solving
-0.3333333334 + x = -1.452966315

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.452966315 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.452966315 + 0.3333333334
x = -1.452966315 + 0.3333333334

Combine like terms: -1.452966315 + 0.3333333334 = -1.1196329816
x = -1.1196329816

Simplifying
x = -1.1196329816

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.7862996484, -1.1196329816}