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

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

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

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

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

Multiply (-4 + x) * (3 + 3x)
(-4(3 + 3x) + x(3 + 3x)) = (x + 2)(x + 6)
((3 * -4 + 3x * -4) + x(3 + 3x)) = (x + 2)(x + 6)
((-12 + -12x) + x(3 + 3x)) = (x + 2)(x + 6)
(-12 + -12x + (3 * x + 3x * x)) = (x + 2)(x + 6)
(-12 + -12x + (3x + 3x2)) = (x + 2)(x + 6)

Combine like terms: -12x + 3x = -9x
(-12 + -9x + 3x2) = (x + 2)(x + 6)

Reorder the terms:
-12 + -9x + 3x2 = (2 + x)(x + 6)

Reorder the terms:
-12 + -9x + 3x2 = (2 + x)(6 + x)

Multiply (2 + x) * (6 + x)
-12 + -9x + 3x2 = (2(6 + x) + x(6 + x))
-12 + -9x + 3x2 = ((6 * 2 + x * 2) + x(6 + x))
-12 + -9x + 3x2 = ((12 + 2x) + x(6 + x))
-12 + -9x + 3x2 = (12 + 2x + (6 * x + x * x))
-12 + -9x + 3x2 = (12 + 2x + (6x + x2))

Combine like terms: 2x + 6x = 8x
-12 + -9x + 3x2 = (12 + 8x + x2)

Solving
-12 + -9x + 3x2 = 12 + 8x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + -12 + -9x + -8x + 3x2 + -1x2 = 12 + 8x + x2 + -12 + -8x + -1x2

Combine like terms: -12 + -12 = -24
-24 + -9x + -8x + 3x2 + -1x2 = 12 + 8x + x2 + -12 + -8x + -1x2

Combine like terms: -9x + -8x = -17x
-24 + -17x + 3x2 + -1x2 = 12 + 8x + x2 + -12 + -8x + -1x2

Combine like terms: 3x2 + -1x2 = 2x2
-24 + -17x + 2x2 = 12 + 8x + x2 + -12 + -8x + -1x2

Reorder the terms:
-24 + -17x + 2x2 = 12 + -12 + 8x + -8x + x2 + -1x2

Combine like terms: 12 + -12 = 0
-24 + -17x + 2x2 = 0 + 8x + -8x + x2 + -1x2
-24 + -17x + 2x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
-24 + -17x + 2x2 = 0 + x2 + -1x2
-24 + -17x + 2x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-24 + -17x + 2x2 = 0

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

Divide each side by '2'.
-12 + -8.5x + x2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8.5x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -8.5x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8.5x + x2 = 0 + 12
-8.5x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8.5x + x2 = 12

The x term is -8.5x.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5x + 18.0625 + x2 = 12 + 18.0625

Reorder the terms:
18.0625 + -8.5x + x2 = 12 + 18.0625

Combine like terms: 12 + 18.0625 = 30.0625
18.0625 + -8.5x + x2 = 30.0625

Factor a perfect square on the left side:
(x + -4.25)(x + -4.25) = 30.0625

Calculate the square root of the right side: 5.48292805

Break this problem into two subproblems by setting 
(x + -4.25) equal to 5.48292805 and -5.48292805.

Subproblem 1
x + -4.25 = 5.48292805

Simplifying
x + -4.25 = 5.48292805

Reorder the terms:
-4.25 + x = 5.48292805

Solving
-4.25 + x = 5.48292805

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = 5.48292805 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = 5.48292805 + 4.25
x = 5.48292805 + 4.25

Combine like terms: 5.48292805 + 4.25 = 9.73292805
x = 9.73292805

Simplifying
x = 9.73292805

Subproblem 2
x + -4.25 = -5.48292805

Simplifying
x + -4.25 = -5.48292805

Reorder the terms:
-4.25 + x = -5.48292805

Solving
-4.25 + x = -5.48292805

Solving for variable 'x'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + x = -5.48292805 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + x = -5.48292805 + 4.25
x = -5.48292805 + 4.25

Combine like terms: -5.48292805 + 4.25 = -1.23292805
x = -1.23292805

Simplifying
x = -1.23292805

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.73292805, -1.23292805}