2(x+3)7x=18-5(x+4)

Solution for 2(x+3)7x=18-5(x+4) equation:

Simplifying
2(x + 3) * 7x = 18 + -5(x + 4)

Reorder the terms:
2(3 + x) * 7x = 18 + -5(x + 4)

Reorder the terms for easier multiplication:
2 * 7x(3 + x) = 18 + -5(x + 4)

Multiply 2 * 7
14x(3 + x) = 18 + -5(x + 4)
(3 * 14x + x * 14x) = 18 + -5(x + 4)
(42x + 14x2) = 18 + -5(x + 4)

Reorder the terms:
42x + 14x2 = 18 + -5(4 + x)
42x + 14x2 = 18 + (4 * -5 + x * -5)
42x + 14x2 = 18 + (-20 + -5x)

Combine like terms: 18 + -20 = -2
42x + 14x2 = -2 + -5x

Solving
42x + 14x2 = -2 + -5x

Solving for variable 'x'.

Reorder the terms:
2 + 42x + 5x + 14x2 = -2 + -5x + 2 + 5x

Combine like terms: 42x + 5x = 47x
2 + 47x + 14x2 = -2 + -5x + 2 + 5x

Reorder the terms:
2 + 47x + 14x2 = -2 + 2 + -5x + 5x

Combine like terms: -2 + 2 = 0
2 + 47x + 14x2 = 0 + -5x + 5x
2 + 47x + 14x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
2 + 47x + 14x2 = 0

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

Divide each side by '14'.
0.1428571429 + 3.357142857x + x2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 3.357142857x + -0.1428571429 + x2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 3.357142857x + x2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 3.357142857x + x2 = 0 + -0.1428571429
3.357142857x + x2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
3.357142857x + x2 = -0.1428571429

The x term is 3.357142857x.  Take half its coefficient (1.678571429).
Square it (2.817602042) and add it to both sides.

Add '2.817602042' to each side of the equation.
3.357142857x + 2.817602042 + x2 = -0.1428571429 + 2.817602042

Reorder the terms:
2.817602042 + 3.357142857x + x2 = -0.1428571429 + 2.817602042

Combine like terms: -0.1428571429 + 2.817602042 = 2.6747448991
2.817602042 + 3.357142857x + x2 = 2.6747448991

Factor a perfect square on the left side:
(x + 1.678571429)(x + 1.678571429) = 2.6747448991

Calculate the square root of the right side: 1.635464735

Break this problem into two subproblems by setting 
(x + 1.678571429) equal to 1.635464735 and -1.635464735.

Subproblem 1
x + 1.678571429 = 1.635464735

Simplifying
x + 1.678571429 = 1.635464735

Reorder the terms:
1.678571429 + x = 1.635464735

Solving
1.678571429 + x = 1.635464735

Solving for variable 'x'.

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

Add '-1.678571429' to each side of the equation.
1.678571429 + -1.678571429 + x = 1.635464735 + -1.678571429

Combine like terms: 1.678571429 + -1.678571429 = 0.000000000
0.000000000 + x = 1.635464735 + -1.678571429
x = 1.635464735 + -1.678571429

Combine like terms: 1.635464735 + -1.678571429 = -0.043106694
x = -0.043106694

Simplifying
x = -0.043106694

Subproblem 2
x + 1.678571429 = -1.635464735

Simplifying
x + 1.678571429 = -1.635464735

Reorder the terms:
1.678571429 + x = -1.635464735

Solving
1.678571429 + x = -1.635464735

Solving for variable 'x'.

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

Add '-1.678571429' to each side of the equation.
1.678571429 + -1.678571429 + x = -1.635464735 + -1.678571429

Combine like terms: 1.678571429 + -1.678571429 = 0.000000000
0.000000000 + x = -1.635464735 + -1.678571429
x = -1.635464735 + -1.678571429

Combine like terms: -1.635464735 + -1.678571429 = -3.314036164
x = -3.314036164

Simplifying
x = -3.314036164

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.043106694, -3.314036164}