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

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

Simplifying
(x + -2)(x + -1) = (x + 4)(2x + 2)

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

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

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

Combine like terms: -2x + -1x = -3x
(2 + -3x + x2) = (x + 4)(2x + 2)

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

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

Multiply (4 + x) * (2 + 2x)
2 + -3x + x2 = (4(2 + 2x) + x(2 + 2x))
2 + -3x + x2 = ((2 * 4 + 2x * 4) + x(2 + 2x))
2 + -3x + x2 = ((8 + 8x) + x(2 + 2x))
2 + -3x + x2 = (8 + 8x + (2 * x + 2x * x))
2 + -3x + x2 = (8 + 8x + (2x + 2x2))

Combine like terms: 8x + 2x = 10x
2 + -3x + x2 = (8 + 10x + 2x2)

Solving
2 + -3x + x2 = 8 + 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
2 + -8 + -3x + -10x + x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

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

Combine like terms: -3x + -10x = -13x
-6 + -13x + x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-6 + -13x + -1x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Reorder the terms:
-6 + -13x + -1x2 = 8 + -8 + 10x + -10x + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
-6 + -13x + -1x2 = 0 + 10x + -10x + 2x2 + -2x2
-6 + -13x + -1x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-6 + -13x + -1x2 = 0 + 2x2 + -2x2
-6 + -13x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + -13x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 13x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 13x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 13x + x2 = 0

Solving
6 + 13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 13x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 13x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 13x + x2 = 0 + -6
13x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
13x + x2 = -6

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = -6 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -6 + 42.25

Combine like terms: -6 + 42.25 = 36.25
42.25 + 13x + x2 = 36.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.020797289 and -6.020797289.

Subproblem 1
x + 6.5 = 6.020797289

Simplifying
x + 6.5 = 6.020797289

Reorder the terms:
6.5 + x = 6.020797289

Solving
6.5 + x = 6.020797289

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.020797289 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.020797289 + -6.5
x = 6.020797289 + -6.5

Combine like terms: 6.020797289 + -6.5 = -0.479202711
x = -0.479202711

Simplifying
x = -0.479202711

Subproblem 2
x + 6.5 = -6.020797289

Simplifying
x + 6.5 = -6.020797289

Reorder the terms:
6.5 + x = -6.020797289

Solving
6.5 + x = -6.020797289

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.020797289 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.020797289 + -6.5
x = -6.020797289 + -6.5

Combine like terms: -6.020797289 + -6.5 = -12.520797289
x = -12.520797289

Simplifying
x = -12.520797289

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.479202711, -12.520797289}
Solution
x = {-0.479202711, -12.520797289}