6(x+24)(x-6)+3(x+12)(x-18)=18(x+45)-(x-36)

Solution for 6(x+24)(x-6)+3(x+12)(x-18)=18(x+45)-(x-36) equation:

Simplifying
6(x + 24)(x + -6) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)

Reorder the terms:
6(24 + x)(x + -6) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)

Reorder the terms:
6(24 + x)(-6 + x) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)

Multiply (24 + x) * (-6 + x)
6(24(-6 + x) + x(-6 + x)) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)
6((-6 * 24 + x * 24) + x(-6 + x)) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)
6((-144 + 24x) + x(-6 + x)) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)
6(-144 + 24x + (-6 * x + x * x)) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)
6(-144 + 24x + (-6x + x2)) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)

Combine like terms: 24x + -6x = 18x
6(-144 + 18x + x2) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)
(-144 * 6 + 18x * 6 + x2 * 6) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)
(-864 + 108x + 6x2) + 3(x + 12)(x + -18) = 18(x + 45) + -1(x + -36)

Reorder the terms:
-864 + 108x + 6x2 + 3(12 + x)(x + -18) = 18(x + 45) + -1(x + -36)

Reorder the terms:
-864 + 108x + 6x2 + 3(12 + x)(-18 + x) = 18(x + 45) + -1(x + -36)

Multiply (12 + x) * (-18 + x)
-864 + 108x + 6x2 + 3(12(-18 + x) + x(-18 + x)) = 18(x + 45) + -1(x + -36)
-864 + 108x + 6x2 + 3((-18 * 12 + x * 12) + x(-18 + x)) = 18(x + 45) + -1(x + -36)
-864 + 108x + 6x2 + 3((-216 + 12x) + x(-18 + x)) = 18(x + 45) + -1(x + -36)
-864 + 108x + 6x2 + 3(-216 + 12x + (-18 * x + x * x)) = 18(x + 45) + -1(x + -36)
-864 + 108x + 6x2 + 3(-216 + 12x + (-18x + x2)) = 18(x + 45) + -1(x + -36)

Combine like terms: 12x + -18x = -6x
-864 + 108x + 6x2 + 3(-216 + -6x + x2) = 18(x + 45) + -1(x + -36)
-864 + 108x + 6x2 + (-216 * 3 + -6x * 3 + x2 * 3) = 18(x + 45) + -1(x + -36)
-864 + 108x + 6x2 + (-648 + -18x + 3x2) = 18(x + 45) + -1(x + -36)

Reorder the terms:
-864 + -648 + 108x + -18x + 6x2 + 3x2 = 18(x + 45) + -1(x + -36)

Combine like terms: -864 + -648 = -1512
-1512 + 108x + -18x + 6x2 + 3x2 = 18(x + 45) + -1(x + -36)

Combine like terms: 108x + -18x = 90x
-1512 + 90x + 6x2 + 3x2 = 18(x + 45) + -1(x + -36)

Combine like terms: 6x2 + 3x2 = 9x2
-1512 + 90x + 9x2 = 18(x + 45) + -1(x + -36)

Reorder the terms:
-1512 + 90x + 9x2 = 18(45 + x) + -1(x + -36)
-1512 + 90x + 9x2 = (45 * 18 + x * 18) + -1(x + -36)
-1512 + 90x + 9x2 = (810 + 18x) + -1(x + -36)

Reorder the terms:
-1512 + 90x + 9x2 = 810 + 18x + -1(-36 + x)
-1512 + 90x + 9x2 = 810 + 18x + (-36 * -1 + x * -1)
-1512 + 90x + 9x2 = 810 + 18x + (36 + -1x)

Reorder the terms:
-1512 + 90x + 9x2 = 810 + 36 + 18x + -1x

Combine like terms: 810 + 36 = 846
-1512 + 90x + 9x2 = 846 + 18x + -1x

Combine like terms: 18x + -1x = 17x
-1512 + 90x + 9x2 = 846 + 17x

Solving
-1512 + 90x + 9x2 = 846 + 17x

Solving for variable 'x'.

Reorder the terms:
-1512 + -846 + 90x + -17x + 9x2 = 846 + 17x + -846 + -17x

Combine like terms: -1512 + -846 = -2358
-2358 + 90x + -17x + 9x2 = 846 + 17x + -846 + -17x

Combine like terms: 90x + -17x = 73x
-2358 + 73x + 9x2 = 846 + 17x + -846 + -17x

Reorder the terms:
-2358 + 73x + 9x2 = 846 + -846 + 17x + -17x

Combine like terms: 846 + -846 = 0
-2358 + 73x + 9x2 = 0 + 17x + -17x
-2358 + 73x + 9x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-2358 + 73x + 9x2 = 0

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

Divide each side by '9'.
-262 + 8.111111111x + x2 = 0

Move the constant term to the right:

Add '262' to each side of the equation.
-262 + 8.111111111x + 262 + x2 = 0 + 262

Reorder the terms:
-262 + 262 + 8.111111111x + x2 = 0 + 262

Combine like terms: -262 + 262 = 0
0 + 8.111111111x + x2 = 0 + 262
8.111111111x + x2 = 0 + 262

Combine like terms: 0 + 262 = 262
8.111111111x + x2 = 262

The x term is 8.111111111x.  Take half its coefficient (4.055555556).
Square it (16.44753087) and add it to both sides.

Add '16.44753087' to each side of the equation.
8.111111111x + 16.44753087 + x2 = 262 + 16.44753087

Reorder the terms:
16.44753087 + 8.111111111x + x2 = 262 + 16.44753087

Combine like terms: 262 + 16.44753087 = 278.44753087
16.44753087 + 8.111111111x + x2 = 278.44753087

Factor a perfect square on the left side:
(x + 4.055555556)(x + 4.055555556) = 278.44753087

Calculate the square root of the right side: 16.686747163

Break this problem into two subproblems by setting 
(x + 4.055555556) equal to 16.686747163 and -16.686747163.

Subproblem 1
x + 4.055555556 = 16.686747163

Simplifying
x + 4.055555556 = 16.686747163

Reorder the terms:
4.055555556 + x = 16.686747163

Solving
4.055555556 + x = 16.686747163

Solving for variable 'x'.

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

Add '-4.055555556' to each side of the equation.
4.055555556 + -4.055555556 + x = 16.686747163 + -4.055555556

Combine like terms: 4.055555556 + -4.055555556 = 0.000000000
0.000000000 + x = 16.686747163 + -4.055555556
x = 16.686747163 + -4.055555556

Combine like terms: 16.686747163 + -4.055555556 = 12.631191607
x = 12.631191607

Simplifying
x = 12.631191607

Subproblem 2
x + 4.055555556 = -16.686747163

Simplifying
x + 4.055555556 = -16.686747163

Reorder the terms:
4.055555556 + x = -16.686747163

Solving
4.055555556 + x = -16.686747163

Solving for variable 'x'.

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

Add '-4.055555556' to each side of the equation.
4.055555556 + -4.055555556 + x = -16.686747163 + -4.055555556

Combine like terms: 4.055555556 + -4.055555556 = 0.000000000
0.000000000 + x = -16.686747163 + -4.055555556
x = -16.686747163 + -4.055555556

Combine like terms: -16.686747163 + -4.055555556 = -20.742302719
x = -20.742302719

Simplifying
x = -20.742302719

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.631191607, -20.742302719}