2(x+1)(x-4)-(x-2)(x-2)=0

Solution for 2(x+1)(x-4)-(x-2)(x-2)=0 equation:

Simplifying
2(x + 1)(x + -4) + -1(x + -2)(x + -2) = 0

Reorder the terms:
2(1 + x)(x + -4) + -1(x + -2)(x + -2) = 0

Reorder the terms:
2(1 + x)(-4 + x) + -1(x + -2)(x + -2) = 0

Multiply (1 + x) * (-4 + x)
2(1(-4 + x) + x(-4 + x)) + -1(x + -2)(x + -2) = 0
2((-4 * 1 + x * 1) + x(-4 + x)) + -1(x + -2)(x + -2) = 0
2((-4 + 1x) + x(-4 + x)) + -1(x + -2)(x + -2) = 0
2(-4 + 1x + (-4 * x + x * x)) + -1(x + -2)(x + -2) = 0
2(-4 + 1x + (-4x + x2)) + -1(x + -2)(x + -2) = 0

Combine like terms: 1x + -4x = -3x
2(-4 + -3x + x2) + -1(x + -2)(x + -2) = 0
(-4 * 2 + -3x * 2 + x2 * 2) + -1(x + -2)(x + -2) = 0
(-8 + -6x + 2x2) + -1(x + -2)(x + -2) = 0

Reorder the terms:
-8 + -6x + 2x2 + -1(-2 + x)(x + -2) = 0

Reorder the terms:
-8 + -6x + 2x2 + -1(-2 + x)(-2 + x) = 0

Multiply (-2 + x) * (-2 + x)
-8 + -6x + 2x2 + -1(-2(-2 + x) + x(-2 + x)) = 0
-8 + -6x + 2x2 + -1((-2 * -2 + x * -2) + x(-2 + x)) = 0
-8 + -6x + 2x2 + -1((4 + -2x) + x(-2 + x)) = 0
-8 + -6x + 2x2 + -1(4 + -2x + (-2 * x + x * x)) = 0
-8 + -6x + 2x2 + -1(4 + -2x + (-2x + x2)) = 0

Combine like terms: -2x + -2x = -4x
-8 + -6x + 2x2 + -1(4 + -4x + x2) = 0
-8 + -6x + 2x2 + (4 * -1 + -4x * -1 + x2 * -1) = 0
-8 + -6x + 2x2 + (-4 + 4x + -1x2) = 0

Reorder the terms:
-8 + -4 + -6x + 4x + 2x2 + -1x2 = 0

Combine like terms: -8 + -4 = -12
-12 + -6x + 4x + 2x2 + -1x2 = 0

Combine like terms: -6x + 4x = -2x
-12 + -2x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
-12 + -2x + 1x2 = 0

Solving
-12 + -2x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -2x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -2x + x2 = 0 + 12

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

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

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 12 + 1

Reorder the terms:
1 + -2x + x2 = 12 + 1

Combine like terms: 12 + 1 = 13
1 + -2x + x2 = 13

Factor a perfect square on the left side:
(x + -1)(x + -1) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -1) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + -1 = 3.605551275

Simplifying
x + -1 = 3.605551275

Reorder the terms:
-1 + x = 3.605551275

Solving
-1 + x = 3.605551275

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.605551275 + 1
x = 3.605551275 + 1

Combine like terms: 3.605551275 + 1 = 4.605551275
x = 4.605551275

Simplifying
x = 4.605551275

Subproblem 2
x + -1 = -3.605551275

Simplifying
x + -1 = -3.605551275

Reorder the terms:
-1 + x = -3.605551275

Solving
-1 + x = -3.605551275

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -3.605551275 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.605551275 + 1
x = -3.605551275 + 1

Combine like terms: -3.605551275 + 1 = -2.605551275
x = -2.605551275

Simplifying
x = -2.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.605551275, -2.605551275}