12(x+3)=4(2x+9)4x

Solution for 12(x+3)=4(2x+9)4x equation:

Simplifying
12(x + 3) = 4(2x + 9) * 4x

Reorder the terms:
12(3 + x) = 4(2x + 9) * 4x
(3 * 12 + x * 12) = 4(2x + 9) * 4x
(36 + 12x) = 4(2x + 9) * 4x

Reorder the terms:
36 + 12x = 4(9 + 2x) * 4x

Reorder the terms for easier multiplication:
36 + 12x = 4 * 4x(9 + 2x)

Multiply 4 * 4
36 + 12x = 16x(9 + 2x)
36 + 12x = (9 * 16x + 2x * 16x)
36 + 12x = (144x + 32x2)

Solving
36 + 12x = 144x + 32x2

Solving for variable 'x'.

Combine like terms: 12x + -144x = -132x
36 + -132x + -32x2 = 144x + 32x2 + -144x + -32x2

Reorder the terms:
36 + -132x + -32x2 = 144x + -144x + 32x2 + -32x2

Combine like terms: 144x + -144x = 0
36 + -132x + -32x2 = 0 + 32x2 + -32x2
36 + -132x + -32x2 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
36 + -132x + -32x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(9 + -33x + -8x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(9 + -33x + -8x2)' equal to zero and attempt to solve:

Simplifying
9 + -33x + -8x2 = 0

Solving
9 + -33x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.125 + 4.125x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 4.125x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 4.125x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 4.125x + x2 = 0 + 1.125
4.125x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
4.125x + x2 = 1.125

The x term is 4.125x.  Take half its coefficient (2.0625).
Square it (4.25390625) and add it to both sides.

Add '4.25390625' to each side of the equation.
4.125x + 4.25390625 + x2 = 1.125 + 4.25390625

Reorder the terms:
4.25390625 + 4.125x + x2 = 1.125 + 4.25390625

Combine like terms: 1.125 + 4.25390625 = 5.37890625
4.25390625 + 4.125x + x2 = 5.37890625

Factor a perfect square on the left side:
(x + 2.0625)(x + 2.0625) = 5.37890625

Calculate the square root of the right side: 2.319246914

Break this problem into two subproblems by setting 
(x + 2.0625) equal to 2.319246914 and -2.319246914.

Subproblem 1
x + 2.0625 = 2.319246914

Simplifying
x + 2.0625 = 2.319246914

Reorder the terms:
2.0625 + x = 2.319246914

Solving
2.0625 + x = 2.319246914

Solving for variable 'x'.

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

Add '-2.0625' to each side of the equation.
2.0625 + -2.0625 + x = 2.319246914 + -2.0625

Combine like terms: 2.0625 + -2.0625 = 0.0000
0.0000 + x = 2.319246914 + -2.0625
x = 2.319246914 + -2.0625

Combine like terms: 2.319246914 + -2.0625 = 0.256746914
x = 0.256746914

Simplifying
x = 0.256746914

Subproblem 2
x + 2.0625 = -2.319246914

Simplifying
x + 2.0625 = -2.319246914

Reorder the terms:
2.0625 + x = -2.319246914

Solving
2.0625 + x = -2.319246914

Solving for variable 'x'.

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

Add '-2.0625' to each side of the equation.
2.0625 + -2.0625 + x = -2.319246914 + -2.0625

Combine like terms: 2.0625 + -2.0625 = 0.0000
0.0000 + x = -2.319246914 + -2.0625
x = -2.319246914 + -2.0625

Combine like terms: -2.319246914 + -2.0625 = -4.381746914
x = -4.381746914

Simplifying
x = -4.381746914

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.256746914, -4.381746914}
Solution
x = {0.256746914, -4.381746914}