7[2(3+4x)]2x=9+2(115x)

Solution for 7[2(3+4x)]2x=9+2(115x) equation:

Simplifying
7[2(3 + 4x)] * 2x = 9 + 2(115x)
7[(3 * 2 + 4x * 2)] * 2x = 9 + 2(115x)
7[(6 + 8x)] * 2x = 9 + 2(115x)

Reorder the terms for easier multiplication:
7 * 2x[6 + 8x] = 9 + 2(115x)

Multiply 7 * 2
14x[6 + 8x] = 9 + 2(115x)
[6 * 14x + 8x * 14x] = 9 + 2(115x)
[84x + 112x2] = 9 + 2(115x)

Remove parenthesis around (115x)
84x + 112x2 = 9 + 2 * 115x

Multiply 2 * 115
84x + 112x2 = 9 + 230x

Solving
84x + 112x2 = 9 + 230x

Solving for variable 'x'.

Reorder the terms:
-9 + 84x + -230x + 112x2 = 9 + 230x + -9 + -230x

Combine like terms: 84x + -230x = -146x
-9 + -146x + 112x2 = 9 + 230x + -9 + -230x

Reorder the terms:
-9 + -146x + 112x2 = 9 + -9 + 230x + -230x

Combine like terms: 9 + -9 = 0
-9 + -146x + 112x2 = 0 + 230x + -230x
-9 + -146x + 112x2 = 230x + -230x

Combine like terms: 230x + -230x = 0
-9 + -146x + 112x2 = 0

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

Divide each side by '112'.
-0.08035714286 + -1.303571429x + x2 = 0

Move the constant term to the right:

Add '0.08035714286' to each side of the equation.
-0.08035714286 + -1.303571429x + 0.08035714286 + x2 = 0 + 0.08035714286

Reorder the terms:
-0.08035714286 + 0.08035714286 + -1.303571429x + x2 = 0 + 0.08035714286

Combine like terms: -0.08035714286 + 0.08035714286 = 0.00000000000
0.00000000000 + -1.303571429x + x2 = 0 + 0.08035714286
-1.303571429x + x2 = 0 + 0.08035714286

Combine like terms: 0 + 0.08035714286 = 0.08035714286
-1.303571429x + x2 = 0.08035714286

The x term is -1.303571429x.  Take half its coefficient (-0.6517857145).
Square it (0.4248246176) and add it to both sides.

Add '0.4248246176' to each side of the equation.
-1.303571429x + 0.4248246176 + x2 = 0.08035714286 + 0.4248246176

Reorder the terms:
0.4248246176 + -1.303571429x + x2 = 0.08035714286 + 0.4248246176

Combine like terms: 0.08035714286 + 0.4248246176 = 0.50518176046
0.4248246176 + -1.303571429x + x2 = 0.50518176046

Factor a perfect square on the left side:
(x + -0.6517857145)(x + -0.6517857145) = 0.50518176046

Calculate the square root of the right side: 0.710761395

Break this problem into two subproblems by setting 
(x + -0.6517857145) equal to 0.710761395 and -0.710761395.

Subproblem 1
x + -0.6517857145 = 0.710761395

Simplifying
x + -0.6517857145 = 0.710761395

Reorder the terms:
-0.6517857145 + x = 0.710761395

Solving
-0.6517857145 + x = 0.710761395

Solving for variable 'x'.

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

Add '0.6517857145' to each side of the equation.
-0.6517857145 + 0.6517857145 + x = 0.710761395 + 0.6517857145

Combine like terms: -0.6517857145 + 0.6517857145 = 0.0000000000
0.0000000000 + x = 0.710761395 + 0.6517857145
x = 0.710761395 + 0.6517857145

Combine like terms: 0.710761395 + 0.6517857145 = 1.3625471095
x = 1.3625471095

Simplifying
x = 1.3625471095

Subproblem 2
x + -0.6517857145 = -0.710761395

Simplifying
x + -0.6517857145 = -0.710761395

Reorder the terms:
-0.6517857145 + x = -0.710761395

Solving
-0.6517857145 + x = -0.710761395

Solving for variable 'x'.

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

Add '0.6517857145' to each side of the equation.
-0.6517857145 + 0.6517857145 + x = -0.710761395 + 0.6517857145

Combine like terms: -0.6517857145 + 0.6517857145 = 0.0000000000
0.0000000000 + x = -0.710761395 + 0.6517857145
x = -0.710761395 + 0.6517857145

Combine like terms: -0.710761395 + 0.6517857145 = -0.0589756805
x = -0.0589756805

Simplifying
x = -0.0589756805

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3625471095, -0.0589756805}