(2x+1)3x-3=116

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Solution for (2x+1)3x-3=116 equation: 


Simplifying
(2x + 1) * 3x + -3 = 116

Reorder the terms:
(1 + 2x) * 3x + -3 = 116

Reorder the terms for easier multiplication:
3x(1 + 2x) + -3 = 116
(1 * 3x + 2x * 3x) + -3 = 116
(3x + 6x2) + -3 = 116

Reorder the terms:
-3 + 3x + 6x2 = 116

Solving
-3 + 3x + 6x2 = 116

Solving for variable 'x'.

Reorder the terms:
-3 + -116 + 3x + 6x2 = 116 + -116

Combine like terms: -3 + -116 = -119
-119 + 3x + 6x2 = 116 + -116

Combine like terms: 116 + -116 = 0
-119 + 3x + 6x2 = 0

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

Divide each side by '6'.
-19.83333333 + 0.5x + x2 = 0

Move the constant term to the right:

Add '19.83333333' to each side of the equation.
-19.83333333 + 0.5x + 19.83333333 + x2 = 0 + 19.83333333

Reorder the terms:
-19.83333333 + 19.83333333 + 0.5x + x2 = 0 + 19.83333333

Combine like terms: -19.83333333 + 19.83333333 = 0.00000000
0.00000000 + 0.5x + x2 = 0 + 19.83333333
0.5x + x2 = 0 + 19.83333333

Combine like terms: 0 + 19.83333333 = 19.83333333
0.5x + x2 = 19.83333333

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 19.83333333 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 19.83333333 + 0.0625

Combine like terms: 19.83333333 + 0.0625 = 19.89583333
0.0625 + 0.5x + x2 = 19.89583333

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 19.89583333

Calculate the square root of the right side: 4.460474563

Break this problem into two subproblems by setting 
(x + 0.25) equal to 4.460474563 and -4.460474563.


Subproblem 1
x + 0.25 = 4.460474563

Simplifying
x + 0.25 = 4.460474563

Reorder the terms:
0.25 + x = 4.460474563

Solving
0.25 + x = 4.460474563

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 4.460474563 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 4.460474563 + -0.25
x = 4.460474563 + -0.25

Combine like terms: 4.460474563 + -0.25 = 4.210474563
x = 4.210474563

Simplifying
x = 4.210474563


Subproblem 2
x + 0.25 = -4.460474563

Simplifying
x + 0.25 = -4.460474563

Reorder the terms:
0.25 + x = -4.460474563

Solving
0.25 + x = -4.460474563

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -4.460474563 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -4.460474563 + -0.25
x = -4.460474563 + -0.25

Combine like terms: -4.460474563 + -0.25 = -4.710474563
x = -4.710474563

Simplifying
x = -4.710474563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.210474563, -4.710474563}

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