x=(x+6)(x+17)

Solution for x=(x+6)(x+17) equation:

Simplifying
x = (x + 6)(x + 17)

Reorder the terms:
x = (6 + x)(x + 17)

Reorder the terms:
x = (6 + x)(17 + x)

Multiply (6 + x) * (17 + x)
x = (6(17 + x) + x(17 + x))
x = ((17 * 6 + x * 6) + x(17 + x))
x = ((102 + 6x) + x(17 + x))
x = (102 + 6x + (17 * x + x * x))
x = (102 + 6x + (17x + x2))

Combine like terms: 6x + 17x = 23x
x = (102 + 23x + x2)

Solving
x = 102 + 23x + x2

Solving for variable 'x'.

Reorder the terms:
-102 + x + -23x + -1x2 = 102 + 23x + x2 + -102 + -23x + -1x2

Combine like terms: x + -23x = -22x
-102 + -22x + -1x2 = 102 + 23x + x2 + -102 + -23x + -1x2

Reorder the terms:
-102 + -22x + -1x2 = 102 + -102 + 23x + -23x + x2 + -1x2

Combine like terms: 102 + -102 = 0
-102 + -22x + -1x2 = 0 + 23x + -23x + x2 + -1x2
-102 + -22x + -1x2 = 23x + -23x + x2 + -1x2

Combine like terms: 23x + -23x = 0
-102 + -22x + -1x2 = 0 + x2 + -1x2
-102 + -22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-102 + -22x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(102 + 22x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(102 + 22x + x2)' equal to zero and attempt to solve:

Simplifying
102 + 22x + x2 = 0

Solving
102 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-102' to each side of the equation.
102 + 22x + -102 + x2 = 0 + -102

Reorder the terms:
102 + -102 + 22x + x2 = 0 + -102

Combine like terms: 102 + -102 = 0
0 + 22x + x2 = 0 + -102
22x + x2 = 0 + -102

Combine like terms: 0 + -102 = -102
22x + x2 = -102

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = -102 + 121

Reorder the terms:
121 + 22x + x2 = -102 + 121

Combine like terms: -102 + 121 = 19
121 + 22x + x2 = 19

Factor a perfect square on the left side:
(x + 11)(x + 11) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 11) equal to 4.358898944 and -4.358898944.

Subproblem 1
x + 11 = 4.358898944

Simplifying
x + 11 = 4.358898944

Reorder the terms:
11 + x = 4.358898944

Solving
11 + x = 4.358898944

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 4.358898944 + -11

Combine like terms: 11 + -11 = 0
0 + x = 4.358898944 + -11
x = 4.358898944 + -11

Combine like terms: 4.358898944 + -11 = -6.641101056
x = -6.641101056

Simplifying
x = -6.641101056

Subproblem 2
x + 11 = -4.358898944

Simplifying
x + 11 = -4.358898944

Reorder the terms:
11 + x = -4.358898944

Solving
11 + x = -4.358898944

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -4.358898944 + -11

Combine like terms: 11 + -11 = 0
0 + x = -4.358898944 + -11
x = -4.358898944 + -11

Combine like terms: -4.358898944 + -11 = -15.358898944
x = -15.358898944

Simplifying
x = -15.358898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.641101056, -15.358898944}
Solution
x = {-6.641101056, -15.358898944}