2(x+18)6(2x+3)=x+3

Solution for 2(x+18)6(2x+3)=x+3 equation:

Simplifying
2(x + 18) * 6(2x + 3) = x + 3

Reorder the terms:
2(18 + x) * 6(2x + 3) = x + 3

Reorder the terms:
2(18 + x) * 6(3 + 2x) = x + 3

Reorder the terms for easier multiplication:
2 * 6(18 + x)(3 + 2x) = x + 3

Multiply 2 * 6
12(18 + x)(3 + 2x) = x + 3

Multiply (18 + x) * (3 + 2x)
12(18(3 + 2x) + x(3 + 2x)) = x + 3
12((3 * 18 + 2x * 18) + x(3 + 2x)) = x + 3
12((54 + 36x) + x(3 + 2x)) = x + 3
12(54 + 36x + (3 * x + 2x * x)) = x + 3
12(54 + 36x + (3x + 2x2)) = x + 3

Combine like terms: 36x + 3x = 39x
12(54 + 39x + 2x2) = x + 3
(54 * 12 + 39x * 12 + 2x2 * 12) = x + 3
(648 + 468x + 24x2) = x + 3

Reorder the terms:
648 + 468x + 24x2 = 3 + x

Solving
648 + 468x + 24x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
648 + -3 + 468x + -1x + 24x2 = 3 + x + -3 + -1x

Combine like terms: 648 + -3 = 645
645 + 468x + -1x + 24x2 = 3 + x + -3 + -1x

Combine like terms: 468x + -1x = 467x
645 + 467x + 24x2 = 3 + x + -3 + -1x

Reorder the terms:
645 + 467x + 24x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
645 + 467x + 24x2 = 0 + x + -1x
645 + 467x + 24x2 = x + -1x

Combine like terms: x + -1x = 0
645 + 467x + 24x2 = 0

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

Divide each side by '24'.
26.875 + 19.45833333x + x2 = 0

Move the constant term to the right:

Add '-26.875' to each side of the equation.
26.875 + 19.45833333x + -26.875 + x2 = 0 + -26.875

Reorder the terms:
26.875 + -26.875 + 19.45833333x + x2 = 0 + -26.875

Combine like terms: 26.875 + -26.875 = 0.000
0.000 + 19.45833333x + x2 = 0 + -26.875
19.45833333x + x2 = 0 + -26.875

Combine like terms: 0 + -26.875 = -26.875
19.45833333x + x2 = -26.875

The x term is 19.45833333x.  Take half its coefficient (9.729166665).
Square it (94.65668400) and add it to both sides.

Add '94.65668400' to each side of the equation.
19.45833333x + 94.65668400 + x2 = -26.875 + 94.65668400

Reorder the terms:
94.65668400 + 19.45833333x + x2 = -26.875 + 94.65668400

Combine like terms: -26.875 + 94.65668400 = 67.781684
94.65668400 + 19.45833333x + x2 = 67.781684

Factor a perfect square on the left side:
(x + 9.729166665)(x + 9.729166665) = 67.781684

Calculate the square root of the right side: 8.232963258

Break this problem into two subproblems by setting 
(x + 9.729166665) equal to 8.232963258 and -8.232963258.

Subproblem 1
x + 9.729166665 = 8.232963258

Simplifying
x + 9.729166665 = 8.232963258

Reorder the terms:
9.729166665 + x = 8.232963258

Solving
9.729166665 + x = 8.232963258

Solving for variable 'x'.

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

Add '-9.729166665' to each side of the equation.
9.729166665 + -9.729166665 + x = 8.232963258 + -9.729166665

Combine like terms: 9.729166665 + -9.729166665 = 0.000000000
0.000000000 + x = 8.232963258 + -9.729166665
x = 8.232963258 + -9.729166665

Combine like terms: 8.232963258 + -9.729166665 = -1.496203407
x = -1.496203407

Simplifying
x = -1.496203407

Subproblem 2
x + 9.729166665 = -8.232963258

Simplifying
x + 9.729166665 = -8.232963258

Reorder the terms:
9.729166665 + x = -8.232963258

Solving
9.729166665 + x = -8.232963258

Solving for variable 'x'.

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

Add '-9.729166665' to each side of the equation.
9.729166665 + -9.729166665 + x = -8.232963258 + -9.729166665

Combine like terms: 9.729166665 + -9.729166665 = 0.000000000
0.000000000 + x = -8.232963258 + -9.729166665
x = -8.232963258 + -9.729166665

Combine like terms: -8.232963258 + -9.729166665 = -17.962129923
x = -17.962129923

Simplifying
x = -17.962129923

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.496203407, -17.962129923}