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

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

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

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

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

Multiply (3 + 2x) * (6 + x)
(3(6 + x) + 2x * (6 + x)) = (x + -9)(x + 2)
((6 * 3 + x * 3) + 2x * (6 + x)) = (x + -9)(x + 2)
((18 + 3x) + 2x * (6 + x)) = (x + -9)(x + 2)
(18 + 3x + (6 * 2x + x * 2x)) = (x + -9)(x + 2)
(18 + 3x + (12x + 2x2)) = (x + -9)(x + 2)

Combine like terms: 3x + 12x = 15x
(18 + 15x + 2x2) = (x + -9)(x + 2)

Reorder the terms:
18 + 15x + 2x2 = (-9 + x)(x + 2)

Reorder the terms:
18 + 15x + 2x2 = (-9 + x)(2 + x)

Multiply (-9 + x) * (2 + x)
18 + 15x + 2x2 = (-9(2 + x) + x(2 + x))
18 + 15x + 2x2 = ((2 * -9 + x * -9) + x(2 + x))
18 + 15x + 2x2 = ((-18 + -9x) + x(2 + x))
18 + 15x + 2x2 = (-18 + -9x + (2 * x + x * x))
18 + 15x + 2x2 = (-18 + -9x + (2x + x2))

Combine like terms: -9x + 2x = -7x
18 + 15x + 2x2 = (-18 + -7x + x2)

Solving
18 + 15x + 2x2 = -18 + -7x + x2

Solving for variable 'x'.

Reorder the terms:
18 + 18 + 15x + 7x + 2x2 + -1x2 = -18 + -7x + x2 + 18 + 7x + -1x2

Combine like terms: 18 + 18 = 36
36 + 15x + 7x + 2x2 + -1x2 = -18 + -7x + x2 + 18 + 7x + -1x2

Combine like terms: 15x + 7x = 22x
36 + 22x + 2x2 + -1x2 = -18 + -7x + x2 + 18 + 7x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
36 + 22x + 1x2 = -18 + -7x + x2 + 18 + 7x + -1x2

Reorder the terms:
36 + 22x + 1x2 = -18 + 18 + -7x + 7x + x2 + -1x2

Combine like terms: -18 + 18 = 0
36 + 22x + 1x2 = 0 + -7x + 7x + x2 + -1x2
36 + 22x + 1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
36 + 22x + 1x2 = 0 + x2 + -1x2
36 + 22x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
36 + 22x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 22x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 22x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 22x + x2 = 0 + -36
22x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
22x + x2 = -36

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -36 + 121

Reorder the terms:
121 + 22x + x2 = -36 + 121

Combine like terms: -36 + 121 = 85
121 + 22x + x2 = 85

Factor a perfect square on the left side:
(x + 11)(x + 11) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 11) equal to 9.219544457 and -9.219544457.

Subproblem 1
x + 11 = 9.219544457

Simplifying
x + 11 = 9.219544457

Reorder the terms:
11 + x = 9.219544457

Solving
11 + x = 9.219544457

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 9.219544457 + -11

Combine like terms: 11 + -11 = 0
0 + x = 9.219544457 + -11
x = 9.219544457 + -11

Combine like terms: 9.219544457 + -11 = -1.780455543
x = -1.780455543

Simplifying
x = -1.780455543

Subproblem 2
x + 11 = -9.219544457

Simplifying
x + 11 = -9.219544457

Reorder the terms:
11 + x = -9.219544457

Solving
11 + x = -9.219544457

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -9.219544457 + -11

Combine like terms: 11 + -11 = 0
0 + x = -9.219544457 + -11
x = -9.219544457 + -11

Combine like terms: -9.219544457 + -11 = -20.219544457
x = -20.219544457

Simplifying
x = -20.219544457

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.780455543, -20.219544457}