(x+2)-(x+3)(x-3)=6(x+4)-15

Solution for (x+2)-(x+3)(x-3)=6(x+4)-15 equation:

Simplifying
(x + 2) + -1(x + 3)(x + -3) = 6(x + 4) + -15

Reorder the terms:
(2 + x) + -1(x + 3)(x + -3) = 6(x + 4) + -15

Remove parenthesis around (2 + x)
2 + x + -1(x + 3)(x + -3) = 6(x + 4) + -15

Reorder the terms:
2 + x + -1(3 + x)(x + -3) = 6(x + 4) + -15

Reorder the terms:
2 + x + -1(3 + x)(-3 + x) = 6(x + 4) + -15

Multiply (3 + x) * (-3 + x)
2 + x + -1(3(-3 + x) + x(-3 + x)) = 6(x + 4) + -15
2 + x + -1((-3 * 3 + x * 3) + x(-3 + x)) = 6(x + 4) + -15
2 + x + -1((-9 + 3x) + x(-3 + x)) = 6(x + 4) + -15
2 + x + -1(-9 + 3x + (-3 * x + x * x)) = 6(x + 4) + -15
2 + x + -1(-9 + 3x + (-3x + x2)) = 6(x + 4) + -15

Combine like terms: 3x + -3x = 0
2 + x + -1(-9 + 0 + x2) = 6(x + 4) + -15
2 + x + -1(-9 + x2) = 6(x + 4) + -15
2 + x + (-9 * -1 + x2 * -1) = 6(x + 4) + -15
2 + x + (9 + -1x2) = 6(x + 4) + -15

Reorder the terms:
2 + 9 + x + -1x2 = 6(x + 4) + -15

Combine like terms: 2 + 9 = 11
11 + x + -1x2 = 6(x + 4) + -15

Reorder the terms:
11 + x + -1x2 = 6(4 + x) + -15
11 + x + -1x2 = (4 * 6 + x * 6) + -15
11 + x + -1x2 = (24 + 6x) + -15

Reorder the terms:
11 + x + -1x2 = 24 + -15 + 6x

Combine like terms: 24 + -15 = 9
11 + x + -1x2 = 9 + 6x

Solving
11 + x + -1x2 = 9 + 6x

Solving for variable 'x'.

Reorder the terms:
11 + -9 + x + -6x + -1x2 = 9 + 6x + -9 + -6x

Combine like terms: 11 + -9 = 2
2 + x + -6x + -1x2 = 9 + 6x + -9 + -6x

Combine like terms: x + -6x = -5x
2 + -5x + -1x2 = 9 + 6x + -9 + -6x

Reorder the terms:
2 + -5x + -1x2 = 9 + -9 + 6x + -6x

Combine like terms: 9 + -9 = 0
2 + -5x + -1x2 = 0 + 6x + -6x
2 + -5x + -1x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
2 + -5x + -1x2 = 0

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

Divide each side by '-1'.
-2 + 5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5x + x2 = 0 + 2
5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
5x + x2 = 2

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + 5x + x2 = 8.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.872281323 and -2.872281323.

Subproblem 1
x + 2.5 = 2.872281323

Simplifying
x + 2.5 = 2.872281323

Reorder the terms:
2.5 + x = 2.872281323

Solving
2.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.872281323 + -2.5
x = 2.872281323 + -2.5

Combine like terms: 2.872281323 + -2.5 = 0.372281323
x = 0.372281323

Simplifying
x = 0.372281323

Subproblem 2
x + 2.5 = -2.872281323

Simplifying
x + 2.5 = -2.872281323

Reorder the terms:
2.5 + x = -2.872281323

Solving
2.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.872281323 + -2.5
x = -2.872281323 + -2.5

Combine like terms: -2.872281323 + -2.5 = -5.372281323
x = -5.372281323

Simplifying
x = -5.372281323

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.372281323, -5.372281323}