2(x+12)2x=3(x-2)

Solution for 2(x+12)2x=3(x-2) equation:

Simplifying
2(x + 12) * 2x = 3(x + -2)

Reorder the terms:
2(12 + x) * 2x = 3(x + -2)

Reorder the terms for easier multiplication:
2 * 2x(12 + x) = 3(x + -2)

Multiply 2 * 2
4x(12 + x) = 3(x + -2)
(12 * 4x + x * 4x) = 3(x + -2)
(48x + 4x2) = 3(x + -2)

Reorder the terms:
48x + 4x2 = 3(-2 + x)
48x + 4x2 = (-2 * 3 + x * 3)
48x + 4x2 = (-6 + 3x)

Solving
48x + 4x2 = -6 + 3x

Solving for variable 'x'.

Reorder the terms:
6 + 48x + -3x + 4x2 = -6 + 3x + 6 + -3x

Combine like terms: 48x + -3x = 45x
6 + 45x + 4x2 = -6 + 3x + 6 + -3x

Reorder the terms:
6 + 45x + 4x2 = -6 + 6 + 3x + -3x

Combine like terms: -6 + 6 = 0
6 + 45x + 4x2 = 0 + 3x + -3x
6 + 45x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
6 + 45x + 4x2 = 0

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

Divide each side by '4'.
1.5 + 11.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 11.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 11.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 11.25x + x2 = 0 + -1.5
11.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
11.25x + x2 = -1.5

The x term is 11.25x.  Take half its coefficient (5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
11.25x + 31.640625 + x2 = -1.5 + 31.640625

Reorder the terms:
31.640625 + 11.25x + x2 = -1.5 + 31.640625

Combine like terms: -1.5 + 31.640625 = 30.140625
31.640625 + 11.25x + x2 = 30.140625

Factor a perfect square on the left side:
(x + 5.625)(x + 5.625) = 30.140625

Calculate the square root of the right side: 5.490047814

Break this problem into two subproblems by setting 
(x + 5.625) equal to 5.490047814 and -5.490047814.

Subproblem 1
x + 5.625 = 5.490047814

Simplifying
x + 5.625 = 5.490047814

Reorder the terms:
5.625 + x = 5.490047814

Solving
5.625 + x = 5.490047814

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = 5.490047814 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = 5.490047814 + -5.625
x = 5.490047814 + -5.625

Combine like terms: 5.490047814 + -5.625 = -0.134952186
x = -0.134952186

Simplifying
x = -0.134952186

Subproblem 2
x + 5.625 = -5.490047814

Simplifying
x + 5.625 = -5.490047814

Reorder the terms:
5.625 + x = -5.490047814

Solving
5.625 + x = -5.490047814

Solving for variable 'x'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + x = -5.490047814 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + x = -5.490047814 + -5.625
x = -5.490047814 + -5.625

Combine like terms: -5.490047814 + -5.625 = -11.115047814
x = -11.115047814

Simplifying
x = -11.115047814

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.134952186, -11.115047814}