(4x+3)(4x+3)-(x-2)(x-2)=(8-x)(8-x)

Solution for (4x+3)(4x+3)-(x-2)(x-2)=(8-x)(8-x) equation:

Simplifying
(4x + 3)(4x + 3) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)

Reorder the terms:
(3 + 4x)(4x + 3) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)

Reorder the terms:
(3 + 4x)(3 + 4x) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)

Multiply (3 + 4x) * (3 + 4x)
(3(3 + 4x) + 4x * (3 + 4x)) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)
((3 * 3 + 4x * 3) + 4x * (3 + 4x)) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)
((9 + 12x) + 4x * (3 + 4x)) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)
(9 + 12x + (3 * 4x + 4x * 4x)) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)
(9 + 12x + (12x + 16x2)) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)

Combine like terms: 12x + 12x = 24x
(9 + 24x + 16x2) + -1(x + -2)(x + -2) = (8 + -1x)(8 + -1x)

Reorder the terms:
9 + 24x + 16x2 + -1(-2 + x)(x + -2) = (8 + -1x)(8 + -1x)

Reorder the terms:
9 + 24x + 16x2 + -1(-2 + x)(-2 + x) = (8 + -1x)(8 + -1x)

Multiply (-2 + x) * (-2 + x)
9 + 24x + 16x2 + -1(-2(-2 + x) + x(-2 + x)) = (8 + -1x)(8 + -1x)
9 + 24x + 16x2 + -1((-2 * -2 + x * -2) + x(-2 + x)) = (8 + -1x)(8 + -1x)
9 + 24x + 16x2 + -1((4 + -2x) + x(-2 + x)) = (8 + -1x)(8 + -1x)
9 + 24x + 16x2 + -1(4 + -2x + (-2 * x + x * x)) = (8 + -1x)(8 + -1x)
9 + 24x + 16x2 + -1(4 + -2x + (-2x + x2)) = (8 + -1x)(8 + -1x)

Combine like terms: -2x + -2x = -4x
9 + 24x + 16x2 + -1(4 + -4x + x2) = (8 + -1x)(8 + -1x)
9 + 24x + 16x2 + (4 * -1 + -4x * -1 + x2 * -1) = (8 + -1x)(8 + -1x)
9 + 24x + 16x2 + (-4 + 4x + -1x2) = (8 + -1x)(8 + -1x)

Reorder the terms:
9 + -4 + 24x + 4x + 16x2 + -1x2 = (8 + -1x)(8 + -1x)

Combine like terms: 9 + -4 = 5
5 + 24x + 4x + 16x2 + -1x2 = (8 + -1x)(8 + -1x)

Combine like terms: 24x + 4x = 28x
5 + 28x + 16x2 + -1x2 = (8 + -1x)(8 + -1x)

Combine like terms: 16x2 + -1x2 = 15x2
5 + 28x + 15x2 = (8 + -1x)(8 + -1x)

Multiply (8 + -1x) * (8 + -1x)
5 + 28x + 15x2 = (8(8 + -1x) + -1x * (8 + -1x))
5 + 28x + 15x2 = ((8 * 8 + -1x * 8) + -1x * (8 + -1x))
5 + 28x + 15x2 = ((64 + -8x) + -1x * (8 + -1x))
5 + 28x + 15x2 = (64 + -8x + (8 * -1x + -1x * -1x))
5 + 28x + 15x2 = (64 + -8x + (-8x + 1x2))

Combine like terms: -8x + -8x = -16x
5 + 28x + 15x2 = (64 + -16x + 1x2)

Solving
5 + 28x + 15x2 = 64 + -16x + 1x2

Solving for variable 'x'.

Reorder the terms:
5 + -64 + 28x + 16x + 15x2 + -1x2 = 64 + -16x + 1x2 + -64 + 16x + -1x2

Combine like terms: 5 + -64 = -59
-59 + 28x + 16x + 15x2 + -1x2 = 64 + -16x + 1x2 + -64 + 16x + -1x2

Combine like terms: 28x + 16x = 44x
-59 + 44x + 15x2 + -1x2 = 64 + -16x + 1x2 + -64 + 16x + -1x2

Combine like terms: 15x2 + -1x2 = 14x2
-59 + 44x + 14x2 = 64 + -16x + 1x2 + -64 + 16x + -1x2

Reorder the terms:
-59 + 44x + 14x2 = 64 + -64 + -16x + 16x + 1x2 + -1x2

Combine like terms: 64 + -64 = 0
-59 + 44x + 14x2 = 0 + -16x + 16x + 1x2 + -1x2
-59 + 44x + 14x2 = -16x + 16x + 1x2 + -1x2

Combine like terms: -16x + 16x = 0
-59 + 44x + 14x2 = 0 + 1x2 + -1x2
-59 + 44x + 14x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-59 + 44x + 14x2 = 0

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

Divide each side by '14'.
-4.214285714 + 3.142857143x + x2 = 0

Move the constant term to the right:

Add '4.214285714' to each side of the equation.
-4.214285714 + 3.142857143x + 4.214285714 + x2 = 0 + 4.214285714

Reorder the terms:
-4.214285714 + 4.214285714 + 3.142857143x + x2 = 0 + 4.214285714

Combine like terms: -4.214285714 + 4.214285714 = 0.000000000
0.000000000 + 3.142857143x + x2 = 0 + 4.214285714
3.142857143x + x2 = 0 + 4.214285714

Combine like terms: 0 + 4.214285714 = 4.214285714
3.142857143x + x2 = 4.214285714

The x term is 3.142857143x.  Take half its coefficient (1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
3.142857143x + 2.469387757 + x2 = 4.214285714 + 2.469387757

Reorder the terms:
2.469387757 + 3.142857143x + x2 = 4.214285714 + 2.469387757

Combine like terms: 4.214285714 + 2.469387757 = 6.683673471
2.469387757 + 3.142857143x + x2 = 6.683673471

Factor a perfect square on the left side:
(x + 1.571428572)(x + 1.571428572) = 6.683673471

Calculate the square root of the right side: 2.585280153

Break this problem into two subproblems by setting 
(x + 1.571428572) equal to 2.585280153 and -2.585280153.

Subproblem 1
x + 1.571428572 = 2.585280153

Simplifying
x + 1.571428572 = 2.585280153

Reorder the terms:
1.571428572 + x = 2.585280153

Solving
1.571428572 + x = 2.585280153

Solving for variable 'x'.

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

Add '-1.571428572' to each side of the equation.
1.571428572 + -1.571428572 + x = 2.585280153 + -1.571428572

Combine like terms: 1.571428572 + -1.571428572 = 0.000000000
0.000000000 + x = 2.585280153 + -1.571428572
x = 2.585280153 + -1.571428572

Combine like terms: 2.585280153 + -1.571428572 = 1.013851581
x = 1.013851581

Simplifying
x = 1.013851581

Subproblem 2
x + 1.571428572 = -2.585280153

Simplifying
x + 1.571428572 = -2.585280153

Reorder the terms:
1.571428572 + x = -2.585280153

Solving
1.571428572 + x = -2.585280153

Solving for variable 'x'.

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

Add '-1.571428572' to each side of the equation.
1.571428572 + -1.571428572 + x = -2.585280153 + -1.571428572

Combine like terms: 1.571428572 + -1.571428572 = 0.000000000
0.000000000 + x = -2.585280153 + -1.571428572
x = -2.585280153 + -1.571428572

Combine like terms: -2.585280153 + -1.571428572 = -4.156708725
x = -4.156708725

Simplifying
x = -4.156708725

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.013851581, -4.156708725}