3(x+3)4x=15-2x+3

Solution for 3(x+3)4x=15-2x+3 equation:

Simplifying
3(x + 3) * 4x = 15 + -2x + 3

Reorder the terms:
3(3 + x) * 4x = 15 + -2x + 3

Reorder the terms for easier multiplication:
3 * 4x(3 + x) = 15 + -2x + 3

Multiply 3 * 4
12x(3 + x) = 15 + -2x + 3
(3 * 12x + x * 12x) = 15 + -2x + 3
(36x + 12x2) = 15 + -2x + 3

Reorder the terms:
36x + 12x2 = 15 + 3 + -2x

Combine like terms: 15 + 3 = 18
36x + 12x2 = 18 + -2x

Solving
36x + 12x2 = 18 + -2x

Solving for variable 'x'.

Reorder the terms:
-18 + 36x + 2x + 12x2 = 18 + -2x + -18 + 2x

Combine like terms: 36x + 2x = 38x
-18 + 38x + 12x2 = 18 + -2x + -18 + 2x

Reorder the terms:
-18 + 38x + 12x2 = 18 + -18 + -2x + 2x

Combine like terms: 18 + -18 = 0
-18 + 38x + 12x2 = 0 + -2x + 2x
-18 + 38x + 12x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-18 + 38x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 19x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + 19x + 6x2)' equal to zero and attempt to solve:

Simplifying
-9 + 19x + 6x2 = 0

Solving
-9 + 19x + 6x2 = 0

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

Divide each side by '6'.
-1.5 + 3.166666667x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 3.166666667x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 3.166666667x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 3.166666667x + x2 = 0 + 1.5
3.166666667x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
3.166666667x + x2 = 1.5

The x term is 3.166666667x.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667x + 2.506944447 + x2 = 1.5 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667x + x2 = 1.5 + 2.506944447

Combine like terms: 1.5 + 2.506944447 = 4.006944447
2.506944447 + 3.166666667x + x2 = 4.006944447

Factor a perfect square on the left side:
(x + 1.583333334)(x + 1.583333334) = 4.006944447

Calculate the square root of the right side: 2.001735359

Break this problem into two subproblems by setting 
(x + 1.583333334) equal to 2.001735359 and -2.001735359.

Subproblem 1
x + 1.583333334 = 2.001735359

Simplifying
x + 1.583333334 = 2.001735359

Reorder the terms:
1.583333334 + x = 2.001735359

Solving
1.583333334 + x = 2.001735359

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = 2.001735359 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = 2.001735359 + -1.583333334
x = 2.001735359 + -1.583333334

Combine like terms: 2.001735359 + -1.583333334 = 0.418402025
x = 0.418402025

Simplifying
x = 0.418402025

Subproblem 2
x + 1.583333334 = -2.001735359

Simplifying
x + 1.583333334 = -2.001735359

Reorder the terms:
1.583333334 + x = -2.001735359

Solving
1.583333334 + x = -2.001735359

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = -2.001735359 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = -2.001735359 + -1.583333334
x = -2.001735359 + -1.583333334

Combine like terms: -2.001735359 + -1.583333334 = -3.585068693
x = -3.585068693

Simplifying
x = -3.585068693

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.418402025, -3.585068693}
Solution
x = {0.418402025, -3.585068693}