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

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

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

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

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

Multiply (-6 + x) * (9 + 2x)
x = (-6(9 + 2x) + x(9 + 2x))
x = ((9 * -6 + 2x * -6) + x(9 + 2x))
x = ((-54 + -12x) + x(9 + 2x))
x = (-54 + -12x + (9 * x + 2x * x))
x = (-54 + -12x + (9x + 2x2))

Combine like terms: -12x + 9x = -3x
x = (-54 + -3x + 2x2)

Solving
x = -54 + -3x + 2x2

Solving for variable 'x'.

Reorder the terms:
54 + x + 3x + -2x2 = -54 + -3x + 2x2 + 54 + 3x + -2x2

Combine like terms: x + 3x = 4x
54 + 4x + -2x2 = -54 + -3x + 2x2 + 54 + 3x + -2x2

Reorder the terms:
54 + 4x + -2x2 = -54 + 54 + -3x + 3x + 2x2 + -2x2

Combine like terms: -54 + 54 = 0
54 + 4x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2
54 + 4x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
54 + 4x + -2x2 = 0 + 2x2 + -2x2
54 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
54 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(27 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
27 + 2x + -1x2 = 0

Solving
27 + 2x + -1x2 = 0

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

Divide each side by '-1'.
-27 + -2x + x2 = 0

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -2x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2x + x2 = 0 + 27
-2x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2x + x2 = 27

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 = 27 + 1

Reorder the terms:
1 + -2x + x2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + -2x + x2 = 28

Factor a perfect square on the left side:
(x + -1)(x + -1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -1) equal to 5.291502622 and -5.291502622.

Subproblem 1
x + -1 = 5.291502622

Simplifying
x + -1 = 5.291502622

Reorder the terms:
-1 + x = 5.291502622

Solving
-1 + x = 5.291502622

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 = 5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.291502622 + 1
x = 5.291502622 + 1

Combine like terms: 5.291502622 + 1 = 6.291502622
x = 6.291502622

Simplifying
x = 6.291502622

Subproblem 2
x + -1 = -5.291502622

Simplifying
x + -1 = -5.291502622

Reorder the terms:
-1 + x = -5.291502622

Solving
-1 + x = -5.291502622

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 = -5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.291502622 + 1
x = -5.291502622 + 1

Combine like terms: -5.291502622 + 1 = -4.291502622
x = -4.291502622

Simplifying
x = -4.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.291502622, -4.291502622}
Solution
x = {6.291502622, -4.291502622}