5x+3(x+6)=2x(x-2)+12

Solution for 5x+3(x+6)=2x(x-2)+12 equation:

Simplifying
5x + 3(x + 6) = 2x(x + -2) + 12

Reorder the terms:
5x + 3(6 + x) = 2x(x + -2) + 12
5x + (6 * 3 + x * 3) = 2x(x + -2) + 12
5x + (18 + 3x) = 2x(x + -2) + 12

Reorder the terms:
18 + 5x + 3x = 2x(x + -2) + 12

Combine like terms: 5x + 3x = 8x
18 + 8x = 2x(x + -2) + 12

Reorder the terms:
18 + 8x = 2x(-2 + x) + 12
18 + 8x = (-2 * 2x + x * 2x) + 12
18 + 8x = (-4x + 2x2) + 12

Reorder the terms:
18 + 8x = 12 + -4x + 2x2

Solving
18 + 8x = 12 + -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
18 + -12 + 8x + 4x + -2x2 = 12 + -4x + 2x2 + -12 + 4x + -2x2

Combine like terms: 18 + -12 = 6
6 + 8x + 4x + -2x2 = 12 + -4x + 2x2 + -12 + 4x + -2x2

Combine like terms: 8x + 4x = 12x
6 + 12x + -2x2 = 12 + -4x + 2x2 + -12 + 4x + -2x2

Reorder the terms:
6 + 12x + -2x2 = 12 + -12 + -4x + 4x + 2x2 + -2x2

Combine like terms: 12 + -12 = 0
6 + 12x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2
6 + 12x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
6 + 12x + -2x2 = 0 + 2x2 + -2x2
6 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 6x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 6x + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + 6x + -1x2 = 0

Solving
3 + 6x + -1x2 = 0

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

Divide each side by '-1'.
-3 + -6x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -6x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -6x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -6x + x2 = 0 + 3
-6x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-6x + x2 = 3

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 3 + 9

Reorder the terms:
9 + -6x + x2 = 3 + 9

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

Factor a perfect square on the left side:
(x + -3)(x + -3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -3) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -3 = 3.464101615

Simplifying
x + -3 = 3.464101615

Reorder the terms:
-3 + x = 3.464101615

Solving
-3 + x = 3.464101615

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.464101615 + 3
x = 3.464101615 + 3

Combine like terms: 3.464101615 + 3 = 6.464101615
x = 6.464101615

Simplifying
x = 6.464101615

Subproblem 2
x + -3 = -3.464101615

Simplifying
x + -3 = -3.464101615

Reorder the terms:
-3 + x = -3.464101615

Solving
-3 + x = -3.464101615

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.464101615 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.464101615 + 3
x = -3.464101615 + 3

Combine like terms: -3.464101615 + 3 = -0.464101615
x = -0.464101615

Simplifying
x = -0.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.464101615, -0.464101615}
Solution
x = {6.464101615, -0.464101615}