3x+12(3x+4)4x-12=

Solution for 3x+12(3x+4)4x-12= equation:

Simplifying
3x + 12(3x + 4) * 4x + -12 = 0

Reorder the terms:
3x + 12(4 + 3x) * 4x + -12 = 0

Reorder the terms for easier multiplication:
3x + 12 * 4x(4 + 3x) + -12 = 0

Multiply 12 * 4
3x + 48x(4 + 3x) + -12 = 0
3x + (4 * 48x + 3x * 48x) + -12 = 0
3x + (192x + 144x2) + -12 = 0

Reorder the terms:
-12 + 3x + 192x + 144x2 = 0

Combine like terms: 3x + 192x = 195x
-12 + 195x + 144x2 = 0

Solving
-12 + 195x + 144x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 65x + 48x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + 65x + 48x2)' equal to zero and attempt to solve:

Simplifying
-4 + 65x + 48x2 = 0

Solving
-4 + 65x + 48x2 = 0

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

Divide each side by '48'.
-0.08333333333 + 1.354166667x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 1.354166667x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 1.354166667x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 1.354166667x + x2 = 0 + 0.08333333333
1.354166667x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
1.354166667x + x2 = 0.08333333333

The x term is 1.354166667x.  Take half its coefficient (0.6770833335).
Square it (0.4584418405) and add it to both sides.

Add '0.4584418405' to each side of the equation.
1.354166667x + 0.4584418405 + x2 = 0.08333333333 + 0.4584418405

Reorder the terms:
0.4584418405 + 1.354166667x + x2 = 0.08333333333 + 0.4584418405

Combine like terms: 0.08333333333 + 0.4584418405 = 0.54177517383
0.4584418405 + 1.354166667x + x2 = 0.54177517383

Factor a perfect square on the left side:
(x + 0.6770833335)(x + 0.6770833335) = 0.54177517383

Calculate the square root of the right side: 0.736053785

Break this problem into two subproblems by setting 
(x + 0.6770833335) equal to 0.736053785 and -0.736053785.

Subproblem 1
x + 0.6770833335 = 0.736053785

Simplifying
x + 0.6770833335 = 0.736053785

Reorder the terms:
0.6770833335 + x = 0.736053785

Solving
0.6770833335 + x = 0.736053785

Solving for variable 'x'.

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

Add '-0.6770833335' to each side of the equation.
0.6770833335 + -0.6770833335 + x = 0.736053785 + -0.6770833335

Combine like terms: 0.6770833335 + -0.6770833335 = 0.0000000000
0.0000000000 + x = 0.736053785 + -0.6770833335
x = 0.736053785 + -0.6770833335

Combine like terms: 0.736053785 + -0.6770833335 = 0.0589704515
x = 0.0589704515

Simplifying
x = 0.0589704515

Subproblem 2
x + 0.6770833335 = -0.736053785

Simplifying
x + 0.6770833335 = -0.736053785

Reorder the terms:
0.6770833335 + x = -0.736053785

Solving
0.6770833335 + x = -0.736053785

Solving for variable 'x'.

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

Add '-0.6770833335' to each side of the equation.
0.6770833335 + -0.6770833335 + x = -0.736053785 + -0.6770833335

Combine like terms: 0.6770833335 + -0.6770833335 = 0.0000000000
0.0000000000 + x = -0.736053785 + -0.6770833335
x = -0.736053785 + -0.6770833335

Combine like terms: -0.736053785 + -0.6770833335 = -1.4131371185
x = -1.4131371185

Simplifying
x = -1.4131371185

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0589704515, -1.4131371185}
Solution
x = {0.0589704515, -1.4131371185}