-3(3+x)4(x-6)=-4

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

Simplifying
-3(3 + x) * 4(x + -6) = -4

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

Reorder the terms for easier multiplication:
-3 * 4(3 + x)(-6 + x) = -4

Multiply -3 * 4
-12(3 + x)(-6 + x) = -4

Multiply (3 + x) * (-6 + x)
-12(3(-6 + x) + x(-6 + x)) = -4
-12((-6 * 3 + x * 3) + x(-6 + x)) = -4
-12((-18 + 3x) + x(-6 + x)) = -4
-12(-18 + 3x + (-6 * x + x * x)) = -4
-12(-18 + 3x + (-6x + x2)) = -4

Combine like terms: 3x + -6x = -3x
-12(-18 + -3x + x2) = -4
(-18 * -12 + -3x * -12 + x2 * -12) = -4
(216 + 36x + -12x2) = -4

Solving
216 + 36x + -12x2 = -4

Solving for variable 'x'.

Reorder the terms:
216 + 4 + 36x + -12x2 = -4 + 4

Combine like terms: 216 + 4 = 220
220 + 36x + -12x2 = -4 + 4

Combine like terms: -4 + 4 = 0
220 + 36x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(55 + 9x + -3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(55 + 9x + -3x2)' equal to zero and attempt to solve:

Simplifying
55 + 9x + -3x2 = 0

Solving
55 + 9x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-18.33333333 + -3x + x2 = 0

Move the constant term to the right:

Add '18.33333333' to each side of the equation.
-18.33333333 + -3x + 18.33333333 + x2 = 0 + 18.33333333

Reorder the terms:
-18.33333333 + 18.33333333 + -3x + x2 = 0 + 18.33333333

Combine like terms: -18.33333333 + 18.33333333 = 0.00000000
0.00000000 + -3x + x2 = 0 + 18.33333333
-3x + x2 = 0 + 18.33333333

Combine like terms: 0 + 18.33333333 = 18.33333333
-3x + x2 = 18.33333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 18.33333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 18.33333333 + 2.25

Combine like terms: 18.33333333 + 2.25 = 20.58333333
2.25 + -3x + x2 = 20.58333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 20.58333333

Calculate the square root of the right side: 4.536885863

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.536885863 and -4.536885863.

Subproblem 1
x + -1.5 = 4.536885863

Simplifying
x + -1.5 = 4.536885863

Reorder the terms:
-1.5 + x = 4.536885863

Solving
-1.5 + x = 4.536885863

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.536885863 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.536885863 + 1.5
x = 4.536885863 + 1.5

Combine like terms: 4.536885863 + 1.5 = 6.036885863
x = 6.036885863

Simplifying
x = 6.036885863

Subproblem 2
x + -1.5 = -4.536885863

Simplifying
x + -1.5 = -4.536885863

Reorder the terms:
-1.5 + x = -4.536885863

Solving
-1.5 + x = -4.536885863

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.536885863 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.536885863 + 1.5
x = -4.536885863 + 1.5

Combine like terms: -4.536885863 + 1.5 = -3.036885863
x = -3.036885863

Simplifying
x = -3.036885863

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.036885863, -3.036885863}
Solution
x = {6.036885863, -3.036885863}