57=(x+9)*(x+3)

Solution for 57=(x+9)*(x+3) equation:

Simplifying
57 = (x + 9)(x + 3)

Reorder the terms:
57 = (9 + x)(x + 3)

Reorder the terms:
57 = (9 + x)(3 + x)

Multiply (9 + x) * (3 + x)
57 = (9(3 + x) + x(3 + x))
57 = ((3 * 9 + x * 9) + x(3 + x))
57 = ((27 + 9x) + x(3 + x))
57 = (27 + 9x + (3 * x + x * x))
57 = (27 + 9x + (3x + x2))

Combine like terms: 9x + 3x = 12x
57 = (27 + 12x + x2)

Solving
57 = 27 + 12x + x2

Solving for variable 'x'.

Combine like terms: 57 + -27 = 30
30 + -12x + -1x2 = 27 + 12x + x2 + -27 + -12x + -1x2

Reorder the terms:
30 + -12x + -1x2 = 27 + -27 + 12x + -12x + x2 + -1x2

Combine like terms: 27 + -27 = 0
30 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
30 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
30 + -12x + -1x2 = 0 + x2 + -1x2
30 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -12x + -1x2 = 0

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

Divide each side by '-1'.
-30 + 12x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 12x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 12x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 12x + x2 = 0 + 30
12x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
12x + x2 = 30

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 30 + 36

Reorder the terms:
36 + 12x + x2 = 30 + 36

Combine like terms: 30 + 36 = 66
36 + 12x + x2 = 66

Factor a perfect square on the left side:
(x + 6)(x + 6) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(x + 6) equal to 8.124038405 and -8.124038405.

Subproblem 1
x + 6 = 8.124038405

Simplifying
x + 6 = 8.124038405

Reorder the terms:
6 + x = 8.124038405

Solving
6 + x = 8.124038405

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 8.124038405 + -6

Combine like terms: 6 + -6 = 0
0 + x = 8.124038405 + -6
x = 8.124038405 + -6

Combine like terms: 8.124038405 + -6 = 2.124038405
x = 2.124038405

Simplifying
x = 2.124038405

Subproblem 2
x + 6 = -8.124038405

Simplifying
x + 6 = -8.124038405

Reorder the terms:
6 + x = -8.124038405

Solving
6 + x = -8.124038405

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -8.124038405 + -6

Combine like terms: 6 + -6 = 0
0 + x = -8.124038405 + -6
x = -8.124038405 + -6

Combine like terms: -8.124038405 + -6 = -14.124038405
x = -14.124038405

Simplifying
x = -14.124038405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.124038405, -14.124038405}