-6x(2x+4)=12-3(4x+8)

Solution for -6x(2x+4)=12-3(4x+8) equation:

Simplifying
-6x(2x + 4) = 12 + -3(4x + 8)

Reorder the terms:
-6x(4 + 2x) = 12 + -3(4x + 8)
(4 * -6x + 2x * -6x) = 12 + -3(4x + 8)
(-24x + -12x2) = 12 + -3(4x + 8)

Reorder the terms:
-24x + -12x2 = 12 + -3(8 + 4x)
-24x + -12x2 = 12 + (8 * -3 + 4x * -3)
-24x + -12x2 = 12 + (-24 + -12x)

Combine like terms: 12 + -24 = -12
-24x + -12x2 = -12 + -12x

Solving
-24x + -12x2 = -12 + -12x

Solving for variable 'x'.

Reorder the terms:
12 + -24x + 12x + -12x2 = -12 + -12x + 12 + 12x

Combine like terms: -24x + 12x = -12x
12 + -12x + -12x2 = -12 + -12x + 12 + 12x

Reorder the terms:
12 + -12x + -12x2 = -12 + 12 + -12x + 12x

Combine like terms: -12 + 12 = 0
12 + -12x + -12x2 = 0 + -12x + 12x
12 + -12x + -12x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
12 + -12x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(1 + -1x + -1x2) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(1 + -1x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + -1x + -1x2 = 0

Solving
1 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x + x2 = 0 + 1
x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
x + x2 = 1

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

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
1.25 + x2 = 1.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + 0.5 = 1.118033989

Simplifying
x + 0.5 = 1.118033989

Reorder the terms:
0.5 + x = 1.118033989

Solving
0.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.118033989 + -0.5
x = 1.118033989 + -0.5

Combine like terms: 1.118033989 + -0.5 = 0.618033989
x = 0.618033989

Simplifying
x = 0.618033989

Subproblem 2
x + 0.5 = -1.118033989

Simplifying
x + 0.5 = -1.118033989

Reorder the terms:
0.5 + x = -1.118033989

Solving
0.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.118033989 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.118033989 + -0.5
x = -1.118033989 + -0.5

Combine like terms: -1.118033989 + -0.5 = -1.618033989
x = -1.618033989

Simplifying
x = -1.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.618033989, -1.618033989}
Solution
x = {0.618033989, -1.618033989}