6(x+5)(x-2)+3(x+10)(x-18)=18(x+50)-(x-36)

Solution for 6(x+5)(x-2)+3(x+10)(x-18)=18(x+50)-(x-36) equation:

Simplifying
6(x + 5)(x + -2) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)

Reorder the terms:
6(5 + x)(x + -2) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)

Reorder the terms:
6(5 + x)(-2 + x) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)

Multiply (5 + x) * (-2 + x)
6(5(-2 + x) + x(-2 + x)) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)
6((-2 * 5 + x * 5) + x(-2 + x)) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)
6((-10 + 5x) + x(-2 + x)) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)
6(-10 + 5x + (-2 * x + x * x)) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)
6(-10 + 5x + (-2x + x2)) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)

Combine like terms: 5x + -2x = 3x
6(-10 + 3x + x2) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)
(-10 * 6 + 3x * 6 + x2 * 6) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)
(-60 + 18x + 6x2) + 3(x + 10)(x + -18) = 18(x + 50) + -1(x + -36)

Reorder the terms:
-60 + 18x + 6x2 + 3(10 + x)(x + -18) = 18(x + 50) + -1(x + -36)

Reorder the terms:
-60 + 18x + 6x2 + 3(10 + x)(-18 + x) = 18(x + 50) + -1(x + -36)

Multiply (10 + x) * (-18 + x)
-60 + 18x + 6x2 + 3(10(-18 + x) + x(-18 + x)) = 18(x + 50) + -1(x + -36)
-60 + 18x + 6x2 + 3((-18 * 10 + x * 10) + x(-18 + x)) = 18(x + 50) + -1(x + -36)
-60 + 18x + 6x2 + 3((-180 + 10x) + x(-18 + x)) = 18(x + 50) + -1(x + -36)
-60 + 18x + 6x2 + 3(-180 + 10x + (-18 * x + x * x)) = 18(x + 50) + -1(x + -36)
-60 + 18x + 6x2 + 3(-180 + 10x + (-18x + x2)) = 18(x + 50) + -1(x + -36)

Combine like terms: 10x + -18x = -8x
-60 + 18x + 6x2 + 3(-180 + -8x + x2) = 18(x + 50) + -1(x + -36)
-60 + 18x + 6x2 + (-180 * 3 + -8x * 3 + x2 * 3) = 18(x + 50) + -1(x + -36)
-60 + 18x + 6x2 + (-540 + -24x + 3x2) = 18(x + 50) + -1(x + -36)

Reorder the terms:
-60 + -540 + 18x + -24x + 6x2 + 3x2 = 18(x + 50) + -1(x + -36)

Combine like terms: -60 + -540 = -600
-600 + 18x + -24x + 6x2 + 3x2 = 18(x + 50) + -1(x + -36)

Combine like terms: 18x + -24x = -6x
-600 + -6x + 6x2 + 3x2 = 18(x + 50) + -1(x + -36)

Combine like terms: 6x2 + 3x2 = 9x2
-600 + -6x + 9x2 = 18(x + 50) + -1(x + -36)

Reorder the terms:
-600 + -6x + 9x2 = 18(50 + x) + -1(x + -36)
-600 + -6x + 9x2 = (50 * 18 + x * 18) + -1(x + -36)
-600 + -6x + 9x2 = (900 + 18x) + -1(x + -36)

Reorder the terms:
-600 + -6x + 9x2 = 900 + 18x + -1(-36 + x)
-600 + -6x + 9x2 = 900 + 18x + (-36 * -1 + x * -1)
-600 + -6x + 9x2 = 900 + 18x + (36 + -1x)

Reorder the terms:
-600 + -6x + 9x2 = 900 + 36 + 18x + -1x

Combine like terms: 900 + 36 = 936
-600 + -6x + 9x2 = 936 + 18x + -1x

Combine like terms: 18x + -1x = 17x
-600 + -6x + 9x2 = 936 + 17x

Solving
-600 + -6x + 9x2 = 936 + 17x

Solving for variable 'x'.

Reorder the terms:
-600 + -936 + -6x + -17x + 9x2 = 936 + 17x + -936 + -17x

Combine like terms: -600 + -936 = -1536
-1536 + -6x + -17x + 9x2 = 936 + 17x + -936 + -17x

Combine like terms: -6x + -17x = -23x
-1536 + -23x + 9x2 = 936 + 17x + -936 + -17x

Reorder the terms:
-1536 + -23x + 9x2 = 936 + -936 + 17x + -17x

Combine like terms: 936 + -936 = 0
-1536 + -23x + 9x2 = 0 + 17x + -17x
-1536 + -23x + 9x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-1536 + -23x + 9x2 = 0

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

Divide each side by '9'.
-170.6666667 + -2.555555556x + x2 = 0

Move the constant term to the right:

Add '170.6666667' to each side of the equation.
-170.6666667 + -2.555555556x + 170.6666667 + x2 = 0 + 170.6666667

Reorder the terms:
-170.6666667 + 170.6666667 + -2.555555556x + x2 = 0 + 170.6666667

Combine like terms: -170.6666667 + 170.6666667 = 0.0000000
0.0000000 + -2.555555556x + x2 = 0 + 170.6666667
-2.555555556x + x2 = 0 + 170.6666667

Combine like terms: 0 + 170.6666667 = 170.6666667
-2.555555556x + x2 = 170.6666667

The x term is -2.555555556x.  Take half its coefficient (-1.277777778).
Square it (1.632716050) and add it to both sides.

Add '1.632716050' to each side of the equation.
-2.555555556x + 1.632716050 + x2 = 170.6666667 + 1.632716050

Reorder the terms:
1.632716050 + -2.555555556x + x2 = 170.6666667 + 1.632716050

Combine like terms: 170.6666667 + 1.632716050 = 172.29938275
1.632716050 + -2.555555556x + x2 = 172.29938275

Factor a perfect square on the left side:
(x + -1.277777778)(x + -1.277777778) = 172.29938275

Calculate the square root of the right side: 13.126285947

Break this problem into two subproblems by setting 
(x + -1.277777778) equal to 13.126285947 and -13.126285947.

Subproblem 1
x + -1.277777778 = 13.126285947

Simplifying
x + -1.277777778 = 13.126285947

Reorder the terms:
-1.277777778 + x = 13.126285947

Solving
-1.277777778 + x = 13.126285947

Solving for variable 'x'.

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

Add '1.277777778' to each side of the equation.
-1.277777778 + 1.277777778 + x = 13.126285947 + 1.277777778

Combine like terms: -1.277777778 + 1.277777778 = 0.000000000
0.000000000 + x = 13.126285947 + 1.277777778
x = 13.126285947 + 1.277777778

Combine like terms: 13.126285947 + 1.277777778 = 14.404063725
x = 14.404063725

Simplifying
x = 14.404063725

Subproblem 2
x + -1.277777778 = -13.126285947

Simplifying
x + -1.277777778 = -13.126285947

Reorder the terms:
-1.277777778 + x = -13.126285947

Solving
-1.277777778 + x = -13.126285947

Solving for variable 'x'.

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

Add '1.277777778' to each side of the equation.
-1.277777778 + 1.277777778 + x = -13.126285947 + 1.277777778

Combine like terms: -1.277777778 + 1.277777778 = 0.000000000
0.000000000 + x = -13.126285947 + 1.277777778
x = -13.126285947 + 1.277777778

Combine like terms: -13.126285947 + 1.277777778 = -11.848508169
x = -11.848508169

Simplifying
x = -11.848508169

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.404063725, -11.848508169}