8x-3=(18x-63)(3x+9)

Solution for 8x-3=(18x-63)(3x+9) equation:

Simplifying
8x + -3 = (18x + -63)(3x + 9)

Reorder the terms:
-3 + 8x = (18x + -63)(3x + 9)

Reorder the terms:
-3 + 8x = (-63 + 18x)(3x + 9)

Reorder the terms:
-3 + 8x = (-63 + 18x)(9 + 3x)

Multiply (-63 + 18x) * (9 + 3x)
-3 + 8x = (-63(9 + 3x) + 18x * (9 + 3x))
-3 + 8x = ((9 * -63 + 3x * -63) + 18x * (9 + 3x))
-3 + 8x = ((-567 + -189x) + 18x * (9 + 3x))
-3 + 8x = (-567 + -189x + (9 * 18x + 3x * 18x))
-3 + 8x = (-567 + -189x + (162x + 54x2))

Combine like terms: -189x + 162x = -27x
-3 + 8x = (-567 + -27x + 54x2)

Solving
-3 + 8x = -567 + -27x + 54x2

Solving for variable 'x'.

Reorder the terms:
-3 + 567 + 8x + 27x + -54x2 = -567 + -27x + 54x2 + 567 + 27x + -54x2

Combine like terms: -3 + 567 = 564
564 + 8x + 27x + -54x2 = -567 + -27x + 54x2 + 567 + 27x + -54x2

Combine like terms: 8x + 27x = 35x
564 + 35x + -54x2 = -567 + -27x + 54x2 + 567 + 27x + -54x2

Reorder the terms:
564 + 35x + -54x2 = -567 + 567 + -27x + 27x + 54x2 + -54x2

Combine like terms: -567 + 567 = 0
564 + 35x + -54x2 = 0 + -27x + 27x + 54x2 + -54x2
564 + 35x + -54x2 = -27x + 27x + 54x2 + -54x2

Combine like terms: -27x + 27x = 0
564 + 35x + -54x2 = 0 + 54x2 + -54x2
564 + 35x + -54x2 = 54x2 + -54x2

Combine like terms: 54x2 + -54x2 = 0
564 + 35x + -54x2 = 0

Begin completing the square.  Divide all terms by
-54 the coefficient of the squared term: 

Divide each side by '-54'.
-10.44444444 + -0.6481481481x + x2 = 0

Move the constant term to the right:

Add '10.44444444' to each side of the equation.
-10.44444444 + -0.6481481481x + 10.44444444 + x2 = 0 + 10.44444444

Reorder the terms:
-10.44444444 + 10.44444444 + -0.6481481481x + x2 = 0 + 10.44444444

Combine like terms: -10.44444444 + 10.44444444 = 0.00000000
0.00000000 + -0.6481481481x + x2 = 0 + 10.44444444
-0.6481481481x + x2 = 0 + 10.44444444

Combine like terms: 0 + 10.44444444 = 10.44444444
-0.6481481481x + x2 = 10.44444444

The x term is -0.6481481481x.  Take half its coefficient (-0.3240740741).
Square it (0.1050240055) and add it to both sides.

Add '0.1050240055' to each side of the equation.
-0.6481481481x + 0.1050240055 + x2 = 10.44444444 + 0.1050240055

Reorder the terms:
0.1050240055 + -0.6481481481x + x2 = 10.44444444 + 0.1050240055

Combine like terms: 10.44444444 + 0.1050240055 = 10.5494684455
0.1050240055 + -0.6481481481x + x2 = 10.5494684455

Factor a perfect square on the left side:
(x + -0.3240740741)(x + -0.3240740741) = 10.5494684455

Calculate the square root of the right side: 3.247994527

Break this problem into two subproblems by setting 
(x + -0.3240740741) equal to 3.247994527 and -3.247994527.

Subproblem 1
x + -0.3240740741 = 3.247994527

Simplifying
x + -0.3240740741 = 3.247994527

Reorder the terms:
-0.3240740741 + x = 3.247994527

Solving
-0.3240740741 + x = 3.247994527

Solving for variable 'x'.

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

Add '0.3240740741' to each side of the equation.
-0.3240740741 + 0.3240740741 + x = 3.247994527 + 0.3240740741

Combine like terms: -0.3240740741 + 0.3240740741 = 0.0000000000
0.0000000000 + x = 3.247994527 + 0.3240740741
x = 3.247994527 + 0.3240740741

Combine like terms: 3.247994527 + 0.3240740741 = 3.5720686011
x = 3.5720686011

Simplifying
x = 3.5720686011

Subproblem 2
x + -0.3240740741 = -3.247994527

Simplifying
x + -0.3240740741 = -3.247994527

Reorder the terms:
-0.3240740741 + x = -3.247994527

Solving
-0.3240740741 + x = -3.247994527

Solving for variable 'x'.

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

Add '0.3240740741' to each side of the equation.
-0.3240740741 + 0.3240740741 + x = -3.247994527 + 0.3240740741

Combine like terms: -0.3240740741 + 0.3240740741 = 0.0000000000
0.0000000000 + x = -3.247994527 + 0.3240740741
x = -3.247994527 + 0.3240740741

Combine like terms: -3.247994527 + 0.3240740741 = -2.9239204529
x = -2.9239204529

Simplifying
x = -2.9239204529

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5720686011, -2.9239204529}