(x+5)(x+-9)-(-2x+2)(x+6)=

Solution for (x+5)(x+-9)-(-2x+2)(x+6)= equation:

Simplifying
(x + 5)(x + -9) + -1(-2x + 2)(x + 6) = 0

Reorder the terms:
(5 + x)(x + -9) + -1(-2x + 2)(x + 6) = 0

Reorder the terms:
(5 + x)(-9 + x) + -1(-2x + 2)(x + 6) = 0

Multiply (5 + x) * (-9 + x)
(5(-9 + x) + x(-9 + x)) + -1(-2x + 2)(x + 6) = 0
((-9 * 5 + x * 5) + x(-9 + x)) + -1(-2x + 2)(x + 6) = 0
((-45 + 5x) + x(-9 + x)) + -1(-2x + 2)(x + 6) = 0
(-45 + 5x + (-9 * x + x * x)) + -1(-2x + 2)(x + 6) = 0
(-45 + 5x + (-9x + x2)) + -1(-2x + 2)(x + 6) = 0

Combine like terms: 5x + -9x = -4x
(-45 + -4x + x2) + -1(-2x + 2)(x + 6) = 0

Reorder the terms:
-45 + -4x + x2 + -1(2 + -2x)(x + 6) = 0

Reorder the terms:
-45 + -4x + x2 + -1(2 + -2x)(6 + x) = 0

Multiply (2 + -2x) * (6 + x)
-45 + -4x + x2 + -1(2(6 + x) + -2x * (6 + x)) = 0
-45 + -4x + x2 + -1((6 * 2 + x * 2) + -2x * (6 + x)) = 0
-45 + -4x + x2 + -1((12 + 2x) + -2x * (6 + x)) = 0
-45 + -4x + x2 + -1(12 + 2x + (6 * -2x + x * -2x)) = 0
-45 + -4x + x2 + -1(12 + 2x + (-12x + -2x2)) = 0

Combine like terms: 2x + -12x = -10x
-45 + -4x + x2 + -1(12 + -10x + -2x2) = 0
-45 + -4x + x2 + (12 * -1 + -10x * -1 + -2x2 * -1) = 0
-45 + -4x + x2 + (-12 + 10x + 2x2) = 0

Reorder the terms:
-45 + -12 + -4x + 10x + x2 + 2x2 = 0

Combine like terms: -45 + -12 = -57
-57 + -4x + 10x + x2 + 2x2 = 0

Combine like terms: -4x + 10x = 6x
-57 + 6x + x2 + 2x2 = 0

Combine like terms: x2 + 2x2 = 3x2
-57 + 6x + 3x2 = 0

Solving
-57 + 6x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-19 + 2x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-19 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-19 + 2x + x2 = 0

Solving
-19 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 2x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 2x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 2x + x2 = 0 + 19
2x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
2x + x2 = 19

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 = 19 + 1

Reorder the terms:
1 + 2x + x2 = 19 + 1

Combine like terms: 19 + 1 = 20
1 + 2x + x2 = 20

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + 1) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + 1 = 4.472135955

Simplifying
x + 1 = 4.472135955

Reorder the terms:
1 + x = 4.472135955

Solving
1 + x = 4.472135955

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 = 4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + x = 4.472135955 + -1
x = 4.472135955 + -1

Combine like terms: 4.472135955 + -1 = 3.472135955
x = 3.472135955

Simplifying
x = 3.472135955

Subproblem 2
x + 1 = -4.472135955

Simplifying
x + 1 = -4.472135955

Reorder the terms:
1 + x = -4.472135955

Solving
1 + x = -4.472135955

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 = -4.472135955 + -1

Combine like terms: 1 + -1 = 0
0 + x = -4.472135955 + -1
x = -4.472135955 + -1

Combine like terms: -4.472135955 + -1 = -5.472135955
x = -5.472135955

Simplifying
x = -5.472135955

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.472135955, -5.472135955}
Solution
x = {3.472135955, -5.472135955}