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

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

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

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

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

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

Multiply 3 * 3
9(4 + x)(-2 + x) = 3

Multiply (4 + x) * (-2 + x)
9(4(-2 + x) + x(-2 + x)) = 3
9((-2 * 4 + x * 4) + x(-2 + x)) = 3
9((-8 + 4x) + x(-2 + x)) = 3
9(-8 + 4x + (-2 * x + x * x)) = 3
9(-8 + 4x + (-2x + x2)) = 3

Combine like terms: 4x + -2x = 2x
9(-8 + 2x + x2) = 3
(-8 * 9 + 2x * 9 + x2 * 9) = 3
(-72 + 18x + 9x2) = 3

Solving
-72 + 18x + 9x2 = 3

Solving for variable 'x'.

Reorder the terms:
-72 + -3 + 18x + 9x2 = 3 + -3

Combine like terms: -72 + -3 = -75
-75 + 18x + 9x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-75 + 18x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + 6x + 3x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-25 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-25 + 6x + 3x2 = 0

Solving
-25 + 6x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 2x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 2x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 8.333333333
2x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
2x + x2 = 8.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 8.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 8.333333333 + 1

Combine like terms: 8.333333333 + 1 = 9.333333333
1 + 2x + x2 = 9.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 9.333333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + 1) equal to 3.055050463 and -3.055050463.

Subproblem 1
x + 1 = 3.055050463

Simplifying
x + 1 = 3.055050463

Reorder the terms:
1 + x = 3.055050463

Solving
1 + x = 3.055050463

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 3.055050463 + -1

Combine like terms: 1 + -1 = 0
0 + x = 3.055050463 + -1
x = 3.055050463 + -1

Combine like terms: 3.055050463 + -1 = 2.055050463
x = 2.055050463

Simplifying
x = 2.055050463

Subproblem 2
x + 1 = -3.055050463

Simplifying
x + 1 = -3.055050463

Reorder the terms:
1 + x = -3.055050463

Solving
1 + x = -3.055050463

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -3.055050463 + -1

Combine like terms: 1 + -1 = 0
0 + x = -3.055050463 + -1
x = -3.055050463 + -1

Combine like terms: -3.055050463 + -1 = -4.055050463
x = -4.055050463

Simplifying
x = -4.055050463

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.055050463, -4.055050463}
Solution
x = {2.055050463, -4.055050463}