2(x-4)1(2x+4)=6(3x+3)

Solution for 2(x-4)1(2x+4)=6(3x+3) equation:

Simplifying
2(x + -4) * 1(2x + 4) = 6(3x + 3)

Reorder the terms:
2(-4 + x) * 1(2x + 4) = 6(3x + 3)

Reorder the terms:
2(-4 + x) * 1(4 + 2x) = 6(3x + 3)

Reorder the terms for easier multiplication:
2 * 1(-4 + x)(4 + 2x) = 6(3x + 3)

Multiply 2 * 1
2(-4 + x)(4 + 2x) = 6(3x + 3)

Multiply (-4 + x) * (4 + 2x)
2(-4(4 + 2x) + x(4 + 2x)) = 6(3x + 3)
2((4 * -4 + 2x * -4) + x(4 + 2x)) = 6(3x + 3)
2((-16 + -8x) + x(4 + 2x)) = 6(3x + 3)
2(-16 + -8x + (4 * x + 2x * x)) = 6(3x + 3)
2(-16 + -8x + (4x + 2x2)) = 6(3x + 3)

Combine like terms: -8x + 4x = -4x
2(-16 + -4x + 2x2) = 6(3x + 3)
(-16 * 2 + -4x * 2 + 2x2 * 2) = 6(3x + 3)
(-32 + -8x + 4x2) = 6(3x + 3)

Reorder the terms:
-32 + -8x + 4x2 = 6(3 + 3x)
-32 + -8x + 4x2 = (3 * 6 + 3x * 6)
-32 + -8x + 4x2 = (18 + 18x)

Solving
-32 + -8x + 4x2 = 18 + 18x

Solving for variable 'x'.

Reorder the terms:
-32 + -18 + -8x + -18x + 4x2 = 18 + 18x + -18 + -18x

Combine like terms: -32 + -18 = -50
-50 + -8x + -18x + 4x2 = 18 + 18x + -18 + -18x

Combine like terms: -8x + -18x = -26x
-50 + -26x + 4x2 = 18 + 18x + -18 + -18x

Reorder the terms:
-50 + -26x + 4x2 = 18 + -18 + 18x + -18x

Combine like terms: 18 + -18 = 0
-50 + -26x + 4x2 = 0 + 18x + -18x
-50 + -26x + 4x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
-50 + -26x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -13x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-25 + -13x + 2x2)' equal to zero and attempt to solve:

Simplifying
-25 + -13x + 2x2 = 0

Solving
-25 + -13x + 2x2 = 0

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

Divide each side by '2'.
-12.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -6.5x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -6.5x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -6.5x + x2 = 0 + 12.5
-6.5x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
-6.5x + x2 = 12.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 12.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 12.5 + 10.5625

Combine like terms: 12.5 + 10.5625 = 23.0625
10.5625 + -6.5x + x2 = 23.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 23.0625

Calculate the square root of the right side: 4.802343178

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.802343178 and -4.802343178.

Subproblem 1
x + -3.25 = 4.802343178

Simplifying
x + -3.25 = 4.802343178

Reorder the terms:
-3.25 + x = 4.802343178

Solving
-3.25 + x = 4.802343178

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 4.802343178 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 4.802343178 + 3.25
x = 4.802343178 + 3.25

Combine like terms: 4.802343178 + 3.25 = 8.052343178
x = 8.052343178

Simplifying
x = 8.052343178

Subproblem 2
x + -3.25 = -4.802343178

Simplifying
x + -3.25 = -4.802343178

Reorder the terms:
-3.25 + x = -4.802343178

Solving
-3.25 + x = -4.802343178

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -4.802343178 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -4.802343178 + 3.25
x = -4.802343178 + 3.25

Combine like terms: -4.802343178 + 3.25 = -1.552343178
x = -1.552343178

Simplifying
x = -1.552343178

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.052343178, -1.552343178}
Solution
x = {8.052343178, -1.552343178}