(x+6)-(x-4)(x-4)=0

Solution for (x+6)-(x-4)(x-4)=0 equation:

Simplifying
(x + 6) + -1(x + -4)(x + -4) = 0

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

Remove parenthesis around (6 + x)
6 + x + -1(x + -4)(x + -4) = 0

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

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

Multiply (-4 + x) * (-4 + x)
6 + x + -1(-4(-4 + x) + x(-4 + x)) = 0
6 + x + -1((-4 * -4 + x * -4) + x(-4 + x)) = 0
6 + x + -1((16 + -4x) + x(-4 + x)) = 0
6 + x + -1(16 + -4x + (-4 * x + x * x)) = 0
6 + x + -1(16 + -4x + (-4x + x2)) = 0

Combine like terms: -4x + -4x = -8x
6 + x + -1(16 + -8x + x2) = 0
6 + x + (16 * -1 + -8x * -1 + x2 * -1) = 0
6 + x + (-16 + 8x + -1x2) = 0

Reorder the terms:
6 + -16 + x + 8x + -1x2 = 0

Combine like terms: 6 + -16 = -10
-10 + x + 8x + -1x2 = 0

Combine like terms: x + 8x = 9x
-10 + 9x + -1x2 = 0

Solving
-10 + 9x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -9x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -9x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -9x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -9x + x2 = 0 + -10
-9x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-9x + x2 = -10

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -10 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + -9x + x2 = 10.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + -4.5 = 3.201562119

Simplifying
x + -4.5 = 3.201562119

Reorder the terms:
-4.5 + x = 3.201562119

Solving
-4.5 + x = 3.201562119

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.201562119 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.201562119 + 4.5
x = 3.201562119 + 4.5

Combine like terms: 3.201562119 + 4.5 = 7.701562119
x = 7.701562119

Simplifying
x = 7.701562119

Subproblem 2
x + -4.5 = -3.201562119

Simplifying
x + -4.5 = -3.201562119

Reorder the terms:
-4.5 + x = -3.201562119

Solving
-4.5 + x = -3.201562119

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.201562119 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.201562119 + 4.5
x = -3.201562119 + 4.5

Combine like terms: -3.201562119 + 4.5 = 1.298437881
x = 1.298437881

Simplifying
x = 1.298437881

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.701562119, 1.298437881}