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

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

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

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

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

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

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

Solving
36 = 24 + 18x + 3x2

Solving for variable 'x'.

Combine like terms: 36 + -24 = 12
12 + -18x + -3x2 = 24 + 18x + 3x2 + -24 + -18x + -3x2

Reorder the terms:
12 + -18x + -3x2 = 24 + -24 + 18x + -18x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
12 + -18x + -3x2 = 0 + 18x + -18x + 3x2 + -3x2
12 + -18x + -3x2 = 18x + -18x + 3x2 + -3x2

Combine like terms: 18x + -18x = 0
12 + -18x + -3x2 = 0 + 3x2 + -3x2
12 + -18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
12 + -18x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -6x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -6x + -1x2)' equal to zero and attempt to solve:

Simplifying
4 + -6x + -1x2 = 0

Solving
4 + -6x + -1x2 = 0

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

Divide each side by '-1'.
-4 + 6x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 6x + x2 = 0 + 4

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

Combine like terms: 0 + 4 = 4
6x + x2 = 4

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 = 4 + 9

Reorder the terms:
9 + 6x + x2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + 6x + x2 = 13

Factor a perfect square on the left side:
(x + 3)(x + 3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 3) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + 3 = 3.605551275

Simplifying
x + 3 = 3.605551275

Reorder the terms:
3 + x = 3.605551275

Solving
3 + x = 3.605551275

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 = 3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + x = 3.605551275 + -3
x = 3.605551275 + -3

Combine like terms: 3.605551275 + -3 = 0.605551275
x = 0.605551275

Simplifying
x = 0.605551275

Subproblem 2
x + 3 = -3.605551275

Simplifying
x + 3 = -3.605551275

Reorder the terms:
3 + x = -3.605551275

Solving
3 + x = -3.605551275

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 = -3.605551275 + -3

Combine like terms: 3 + -3 = 0
0 + x = -3.605551275 + -3
x = -3.605551275 + -3

Combine like terms: -3.605551275 + -3 = -6.605551275
x = -6.605551275

Simplifying
x = -6.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.605551275, -6.605551275}
Solution
x = {0.605551275, -6.605551275}