6-(3x-9)=(x+7)(x-2)

Solution for 6-(3x-9)=(x+7)(x-2) equation:

Simplifying
6 + -1(3x + -9) = (x + 7)(x + -2)

Reorder the terms:
6 + -1(-9 + 3x) = (x + 7)(x + -2)
6 + (-9 * -1 + 3x * -1) = (x + 7)(x + -2)
6 + (9 + -3x) = (x + 7)(x + -2)

Combine like terms: 6 + 9 = 15
15 + -3x = (x + 7)(x + -2)

Reorder the terms:
15 + -3x = (7 + x)(x + -2)

Reorder the terms:
15 + -3x = (7 + x)(-2 + x)

Multiply (7 + x) * (-2 + x)
15 + -3x = (7(-2 + x) + x(-2 + x))
15 + -3x = ((-2 * 7 + x * 7) + x(-2 + x))
15 + -3x = ((-14 + 7x) + x(-2 + x))
15 + -3x = (-14 + 7x + (-2 * x + x * x))
15 + -3x = (-14 + 7x + (-2x + x2))

Combine like terms: 7x + -2x = 5x
15 + -3x = (-14 + 5x + x2)

Solving
15 + -3x = -14 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
15 + 14 + -3x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: 15 + 14 = 29
29 + -3x + -5x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Combine like terms: -3x + -5x = -8x
29 + -8x + -1x2 = -14 + 5x + x2 + 14 + -5x + -1x2

Reorder the terms:
29 + -8x + -1x2 = -14 + 14 + 5x + -5x + x2 + -1x2

Combine like terms: -14 + 14 = 0
29 + -8x + -1x2 = 0 + 5x + -5x + x2 + -1x2
29 + -8x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
29 + -8x + -1x2 = 0 + x2 + -1x2
29 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
29 + -8x + -1x2 = 0

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

Divide each side by '-1'.
-29 + 8x + x2 = 0

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 8x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + 8x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 8x + x2 = 0 + 29
8x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
8x + x2 = 29

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 29 + 16

Reorder the terms:
16 + 8x + x2 = 29 + 16

Combine like terms: 29 + 16 = 45
16 + 8x + x2 = 45

Factor a perfect square on the left side:
(x + 4)(x + 4) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + 4) equal to 6.708203933 and -6.708203933.

Subproblem 1
x + 4 = 6.708203933

Simplifying
x + 4 = 6.708203933

Reorder the terms:
4 + x = 6.708203933

Solving
4 + x = 6.708203933

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 6.708203933 + -4

Combine like terms: 4 + -4 = 0
0 + x = 6.708203933 + -4
x = 6.708203933 + -4

Combine like terms: 6.708203933 + -4 = 2.708203933
x = 2.708203933

Simplifying
x = 2.708203933

Subproblem 2
x + 4 = -6.708203933

Simplifying
x + 4 = -6.708203933

Reorder the terms:
4 + x = -6.708203933

Solving
4 + x = -6.708203933

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -6.708203933 + -4

Combine like terms: 4 + -4 = 0
0 + x = -6.708203933 + -4
x = -6.708203933 + -4

Combine like terms: -6.708203933 + -4 = -10.708203933
x = -10.708203933

Simplifying
x = -10.708203933

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.708203933, -10.708203933}