(x+5)*(4x-4)=(x+1)*(x+1)

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Solution for (x+5)*(4x-4)=(x+1)*(x+1) equation: 


Simplifying
(x + 5)(4x + -4) = (x + 1)(x + 1)

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

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

Multiply (5 + x) * (-4 + 4x)
(5(-4 + 4x) + x(-4 + 4x)) = (x + 1)(x + 1)
((-4 * 5 + 4x * 5) + x(-4 + 4x)) = (x + 1)(x + 1)
((-20 + 20x) + x(-4 + 4x)) = (x + 1)(x + 1)
(-20 + 20x + (-4 * x + 4x * x)) = (x + 1)(x + 1)
(-20 + 20x + (-4x + 4x2)) = (x + 1)(x + 1)

Combine like terms: 20x + -4x = 16x
(-20 + 16x + 4x2) = (x + 1)(x + 1)

Reorder the terms:
-20 + 16x + 4x2 = (1 + x)(x + 1)

Reorder the terms:
-20 + 16x + 4x2 = (1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
-20 + 16x + 4x2 = (1(1 + x) + x(1 + x))
-20 + 16x + 4x2 = ((1 * 1 + x * 1) + x(1 + x))
-20 + 16x + 4x2 = ((1 + 1x) + x(1 + x))
-20 + 16x + 4x2 = (1 + 1x + (1 * x + x * x))
-20 + 16x + 4x2 = (1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
-20 + 16x + 4x2 = (1 + 2x + x2)

Solving
-20 + 16x + 4x2 = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-20 + -1 + 16x + -2x + 4x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -20 + -1 = -21
-21 + 16x + -2x + 4x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 16x + -2x = 14x
-21 + 14x + 4x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 4x2 + -1x2 = 3x2
-21 + 14x + 3x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
-21 + 14x + 3x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-21 + 14x + 3x2 = 0 + 2x + -2x + x2 + -1x2
-21 + 14x + 3x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-21 + 14x + 3x2 = 0 + x2 + -1x2
-21 + 14x + 3x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-21 + 14x + 3x2 = 0

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

Divide each side by '3'.
-7 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 4.666666667x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 4.666666667x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 4.666666667x + x2 = 0 + 7
4.666666667x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
4.666666667x + x2 = 7

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 7 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 7 + 5.444444448

Combine like terms: 7 + 5.444444448 = 12.444444448
5.444444448 + 4.666666667x + x2 = 12.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 12.444444448

Calculate the square root of the right side: 3.527668415

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 3.527668415 and -3.527668415.


Subproblem 1
x + 2.333333334 = 3.527668415

Simplifying
x + 2.333333334 = 3.527668415

Reorder the terms:
2.333333334 + x = 3.527668415

Solving
2.333333334 + x = 3.527668415

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 3.527668415 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 3.527668415 + -2.333333334
x = 3.527668415 + -2.333333334

Combine like terms: 3.527668415 + -2.333333334 = 1.194335081
x = 1.194335081

Simplifying
x = 1.194335081


Subproblem 2
x + 2.333333334 = -3.527668415

Simplifying
x + 2.333333334 = -3.527668415

Reorder the terms:
2.333333334 + x = -3.527668415

Solving
2.333333334 + x = -3.527668415

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -3.527668415 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -3.527668415 + -2.333333334
x = -3.527668415 + -2.333333334

Combine like terms: -3.527668415 + -2.333333334 = -5.861001749
x = -5.861001749

Simplifying
x = -5.861001749


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.194335081, -5.861001749}

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