(x-9)(x+2)-(2x-6)(x+4)=

Solution for (x-9)(x+2)-(2x-6)(x+4)= equation:

Simplifying
(x + -9)(x + 2) + -1(2x + -6)(x + 4) = 0

Reorder the terms:
(-9 + x)(x + 2) + -1(2x + -6)(x + 4) = 0

Reorder the terms:
(-9 + x)(2 + x) + -1(2x + -6)(x + 4) = 0

Multiply (-9 + x) * (2 + x)
(-9(2 + x) + x(2 + x)) + -1(2x + -6)(x + 4) = 0
((2 * -9 + x * -9) + x(2 + x)) + -1(2x + -6)(x + 4) = 0
((-18 + -9x) + x(2 + x)) + -1(2x + -6)(x + 4) = 0
(-18 + -9x + (2 * x + x * x)) + -1(2x + -6)(x + 4) = 0
(-18 + -9x + (2x + x2)) + -1(2x + -6)(x + 4) = 0

Combine like terms: -9x + 2x = -7x
(-18 + -7x + x2) + -1(2x + -6)(x + 4) = 0

Reorder the terms:
-18 + -7x + x2 + -1(-6 + 2x)(x + 4) = 0

Reorder the terms:
-18 + -7x + x2 + -1(-6 + 2x)(4 + x) = 0

Multiply (-6 + 2x) * (4 + x)
-18 + -7x + x2 + -1(-6(4 + x) + 2x * (4 + x)) = 0
-18 + -7x + x2 + -1((4 * -6 + x * -6) + 2x * (4 + x)) = 0
-18 + -7x + x2 + -1((-24 + -6x) + 2x * (4 + x)) = 0
-18 + -7x + x2 + -1(-24 + -6x + (4 * 2x + x * 2x)) = 0
-18 + -7x + x2 + -1(-24 + -6x + (8x + 2x2)) = 0

Combine like terms: -6x + 8x = 2x
-18 + -7x + x2 + -1(-24 + 2x + 2x2) = 0
-18 + -7x + x2 + (-24 * -1 + 2x * -1 + 2x2 * -1) = 0
-18 + -7x + x2 + (24 + -2x + -2x2) = 0

Reorder the terms:
-18 + 24 + -7x + -2x + x2 + -2x2 = 0

Combine like terms: -18 + 24 = 6
6 + -7x + -2x + x2 + -2x2 = 0

Combine like terms: -7x + -2x = -9x
6 + -9x + x2 + -2x2 = 0

Combine like terms: x2 + -2x2 = -1x2
6 + -9x + -1x2 = 0

Solving
6 + -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'.
-6 + 9x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 9x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 9x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 9x + x2 = 0 + 6
9x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
9x + x2 = 6

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 = 6 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + 9x + x2 = 26.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
x + 4.5 = 5.123475383

Simplifying
x + 4.5 = 5.123475383

Reorder the terms:
4.5 + x = 5.123475383

Solving
4.5 + x = 5.123475383

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 = 5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5.123475383 + -4.5
x = 5.123475383 + -4.5

Combine like terms: 5.123475383 + -4.5 = 0.623475383
x = 0.623475383

Simplifying
x = 0.623475383

Subproblem 2
x + 4.5 = -5.123475383

Simplifying
x + 4.5 = -5.123475383

Reorder the terms:
4.5 + x = -5.123475383

Solving
4.5 + x = -5.123475383

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 = -5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5.123475383 + -4.5
x = -5.123475383 + -4.5

Combine like terms: -5.123475383 + -4.5 = -9.623475383
x = -9.623475383

Simplifying
x = -9.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.623475383, -9.623475383}