(3x-1)(2x-2)=(x-4)2+7

Solution for (3x-1)(2x-2)=(x-4)2+7 equation:

Simplifying
(3x + -1)(2x + -2) = (x + -4) * 2 + 7

Reorder the terms:
(-1 + 3x)(2x + -2) = (x + -4) * 2 + 7

Reorder the terms:
(-1 + 3x)(-2 + 2x) = (x + -4) * 2 + 7

Multiply (-1 + 3x) * (-2 + 2x)
(-1(-2 + 2x) + 3x * (-2 + 2x)) = (x + -4) * 2 + 7
((-2 * -1 + 2x * -1) + 3x * (-2 + 2x)) = (x + -4) * 2 + 7
((2 + -2x) + 3x * (-2 + 2x)) = (x + -4) * 2 + 7
(2 + -2x + (-2 * 3x + 2x * 3x)) = (x + -4) * 2 + 7
(2 + -2x + (-6x + 6x2)) = (x + -4) * 2 + 7

Combine like terms: -2x + -6x = -8x
(2 + -8x + 6x2) = (x + -4) * 2 + 7

Reorder the terms:
2 + -8x + 6x2 = (-4 + x) * 2 + 7

Reorder the terms for easier multiplication:
2 + -8x + 6x2 = 2(-4 + x) + 7
2 + -8x + 6x2 = (-4 * 2 + x * 2) + 7
2 + -8x + 6x2 = (-8 + 2x) + 7

Reorder the terms:
2 + -8x + 6x2 = -8 + 7 + 2x

Combine like terms: -8 + 7 = -1
2 + -8x + 6x2 = -1 + 2x

Solving
2 + -8x + 6x2 = -1 + 2x

Solving for variable 'x'.

Reorder the terms:
2 + 1 + -8x + -2x + 6x2 = -1 + 2x + 1 + -2x

Combine like terms: 2 + 1 = 3
3 + -8x + -2x + 6x2 = -1 + 2x + 1 + -2x

Combine like terms: -8x + -2x = -10x
3 + -10x + 6x2 = -1 + 2x + 1 + -2x

Reorder the terms:
3 + -10x + 6x2 = -1 + 1 + 2x + -2x

Combine like terms: -1 + 1 = 0
3 + -10x + 6x2 = 0 + 2x + -2x
3 + -10x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
3 + -10x + 6x2 = 0

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

Divide each side by '6'.
0.5 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.666666667x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.666666667x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.666666667x + x2 = 0 + -0.5
-1.666666667x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.666666667x + x2 = -0.5

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.5 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.5 + 0.6944444447

Combine like terms: -0.5 + 0.6944444447 = 0.1944444447
0.6944444447 + -1.666666667x + x2 = 0.1944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.1944444447

Calculate the square root of the right side: 0.440958552

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.440958552 and -0.440958552.

Subproblem 1
x + -0.8333333335 = 0.440958552

Simplifying
x + -0.8333333335 = 0.440958552

Reorder the terms:
-0.8333333335 + x = 0.440958552

Solving
-0.8333333335 + x = 0.440958552

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 0.440958552 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 0.440958552 + 0.8333333335
x = 0.440958552 + 0.8333333335

Combine like terms: 0.440958552 + 0.8333333335 = 1.2742918855
x = 1.2742918855

Simplifying
x = 1.2742918855

Subproblem 2
x + -0.8333333335 = -0.440958552

Simplifying
x + -0.8333333335 = -0.440958552

Reorder the terms:
-0.8333333335 + x = -0.440958552

Solving
-0.8333333335 + x = -0.440958552

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -0.440958552 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -0.440958552 + 0.8333333335
x = -0.440958552 + 0.8333333335

Combine like terms: -0.440958552 + 0.8333333335 = 0.3923747815
x = 0.3923747815

Simplifying
x = 0.3923747815

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2742918855, 0.3923747815}