36=.50(3x+6)(x+4)

Solution for 36=.50(3x+6)(x+4) equation:

Simplifying
36 = 0.50(3x + 6)(x + 4)

Reorder the terms:
36 = 0.50(6 + 3x)(x + 4)

Reorder the terms:
36 = 0.50(6 + 3x)(4 + x)

Multiply (6 + 3x) * (4 + x)
36 = 0.50(6(4 + x) + 3x * (4 + x))
36 = 0.50((4 * 6 + x * 6) + 3x * (4 + x))
36 = 0.50((24 + 6x) + 3x * (4 + x))
36 = 0.50(24 + 6x + (4 * 3x + x * 3x))
36 = 0.50(24 + 6x + (12x + 3x2))

Combine like terms: 6x + 12x = 18x
36 = 0.50(24 + 18x + 3x2)
36 = (24 * 0.50 + 18x * 0.50 + 3x2 * 0.50)
36 = (12 + 9x + 1.5x2)

Solving
36 = 12 + 9x + 1.5x2

Solving for variable 'x'.

Combine like terms: 36 + -12 = 24
24 + -9x + -1.5x2 = 12 + 9x + 1.5x2 + -12 + -9x + -1.5x2

Reorder the terms:
24 + -9x + -1.5x2 = 12 + -12 + 9x + -9x + 1.5x2 + -1.5x2

Combine like terms: 12 + -12 = 0
24 + -9x + -1.5x2 = 0 + 9x + -9x + 1.5x2 + -1.5x2
24 + -9x + -1.5x2 = 9x + -9x + 1.5x2 + -1.5x2

Combine like terms: 9x + -9x = 0
24 + -9x + -1.5x2 = 0 + 1.5x2 + -1.5x2
24 + -9x + -1.5x2 = 1.5x2 + -1.5x2

Combine like terms: 1.5x2 + -1.5x2 = 0.0
24 + -9x + -1.5x2 = 0.0

Begin completing the square.  Divide all terms by
-1.5 the coefficient of the squared term: 

Divide each side by '-1.5'.
-16 + 6x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 6x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 6x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 6x + x2 = 0 + 16
6x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
6x + x2 = 16

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 = 16 + 9

Reorder the terms:
9 + 6x + x2 = 16 + 9

Combine like terms: 16 + 9 = 25
9 + 6x + x2 = 25

Factor a perfect square on the left side:
(x + 3)(x + 3) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 3) equal to 5 and -5.

Subproblem 1
x + 3 = 5

Simplifying
x + 3 = 5

Reorder the terms:
3 + x = 5

Solving
3 + x = 5

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 = 5 + -3

Combine like terms: 3 + -3 = 0
0 + x = 5 + -3
x = 5 + -3

Combine like terms: 5 + -3 = 2
x = 2

Simplifying
x = 2

Subproblem 2
x + 3 = -5

Simplifying
x + 3 = -5

Reorder the terms:
3 + x = -5

Solving
3 + x = -5

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 = -5 + -3

Combine like terms: 3 + -3 = 0
0 + x = -5 + -3
x = -5 + -3

Combine like terms: -5 + -3 = -8
x = -8

Simplifying
x = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -8}