(x-3)(x^2+3x+9)=x(x-8)(x+9)

Solution for (x-3)(x^2+3x+9)=x(x-8)(x+9) equation:

Simplifying
(x + -3)(x2 + 3x + 9) = x(x + -8)(x + 9)

Reorder the terms:
(-3 + x)(x2 + 3x + 9) = x(x + -8)(x + 9)

Reorder the terms:
(-3 + x)(9 + 3x + x2) = x(x + -8)(x + 9)

Multiply (-3 + x) * (9 + 3x + x2)
(-3(9 + 3x + x2) + x(9 + 3x + x2)) = x(x + -8)(x + 9)
((9 * -3 + 3x * -3 + x2 * -3) + x(9 + 3x + x2)) = x(x + -8)(x + 9)
((-27 + -9x + -3x2) + x(9 + 3x + x2)) = x(x + -8)(x + 9)
(-27 + -9x + -3x2 + (9 * x + 3x * x + x2 * x)) = x(x + -8)(x + 9)
(-27 + -9x + -3x2 + (9x + 3x2 + x3)) = x(x + -8)(x + 9)

Reorder the terms:
(-27 + -9x + 9x + -3x2 + 3x2 + x3) = x(x + -8)(x + 9)

Combine like terms: -9x + 9x = 0
(-27 + 0 + -3x2 + 3x2 + x3) = x(x + -8)(x + 9)
(-27 + -3x2 + 3x2 + x3) = x(x + -8)(x + 9)

Combine like terms: -3x2 + 3x2 = 0
(-27 + 0 + x3) = x(x + -8)(x + 9)
(-27 + x3) = x(x + -8)(x + 9)

Reorder the terms:
-27 + x3 = x(-8 + x)(x + 9)

Reorder the terms:
-27 + x3 = x(-8 + x)(9 + x)

Multiply (-8 + x) * (9 + x)
-27 + x3 = x(-8(9 + x) + x(9 + x))
-27 + x3 = x((9 * -8 + x * -8) + x(9 + x))
-27 + x3 = x((-72 + -8x) + x(9 + x))
-27 + x3 = x(-72 + -8x + (9 * x + x * x))
-27 + x3 = x(-72 + -8x + (9x + x2))

Combine like terms: -8x + 9x = 1x
-27 + x3 = x(-72 + 1x + x2)
-27 + x3 = (-72 * x + 1x * x + x2 * x)
-27 + x3 = (-72x + 1x2 + x3)

Add '-1x3' to each side of the equation.
-27 + x3 + -1x3 = -72x + 1x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-27 + 0 = -72x + 1x2 + x3 + -1x3
-27 = -72x + 1x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-27 = -72x + 1x2 + 0
-27 = -72x + 1x2

Solving
-27 = -72x + 1x2

Solving for variable 'x'.

Reorder the terms:
-27 + 72x + -1x2 = -72x + 72x + 1x2 + -1x2

Combine like terms: -72x + 72x = 0
-27 + 72x + -1x2 = 0 + 1x2 + -1x2
-27 + 72x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-27 + 72x + -1x2 = 0

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

Divide each side by '-1'.
27 + -72x + x2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -72x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -72x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -72x + x2 = 0 + -27
-72x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-72x + x2 = -27

The x term is -72x.  Take half its coefficient (-36).
Square it (1296) and add it to both sides.

Add '1296' to each side of the equation.
-72x + 1296 + x2 = -27 + 1296

Reorder the terms:
1296 + -72x + x2 = -27 + 1296

Combine like terms: -27 + 1296 = 1269
1296 + -72x + x2 = 1269

Factor a perfect square on the left side:
(x + -36)(x + -36) = 1269

Calculate the square root of the right side: 35.623026261

Break this problem into two subproblems by setting 
(x + -36) equal to 35.623026261 and -35.623026261.

Subproblem 1
x + -36 = 35.623026261

Simplifying
x + -36 = 35.623026261

Reorder the terms:
-36 + x = 35.623026261

Solving
-36 + x = 35.623026261

Solving for variable 'x'.

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

Add '36' to each side of the equation.
-36 + 36 + x = 35.623026261 + 36

Combine like terms: -36 + 36 = 0
0 + x = 35.623026261 + 36
x = 35.623026261 + 36

Combine like terms: 35.623026261 + 36 = 71.623026261
x = 71.623026261

Simplifying
x = 71.623026261

Subproblem 2
x + -36 = -35.623026261

Simplifying
x + -36 = -35.623026261

Reorder the terms:
-36 + x = -35.623026261

Solving
-36 + x = -35.623026261

Solving for variable 'x'.

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

Add '36' to each side of the equation.
-36 + 36 + x = -35.623026261 + 36

Combine like terms: -36 + 36 = 0
0 + x = -35.623026261 + 36
x = -35.623026261 + 36

Combine like terms: -35.623026261 + 36 = 0.376973739
x = 0.376973739

Simplifying
x = 0.376973739

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {71.623026261, 0.376973739}