0=x^2+15x+6

Solution for 0=x^2+15x+6 equation:

Simplifying
0 = x2 + 15x + 6

Reorder the terms:
0 = 6 + 15x + x2

Solving
0 = 6 + 15x + x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -15x + -1x2 = 6 + 15x + x2 + -6 + -15x + -1x2

Reorder the terms:
-6 + -15x + -1x2 = 6 + -6 + 15x + -15x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-6 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2
-6 + -15x + -1x2 = 15x + -15x + x2 + -1x2

Combine like terms: 15x + -15x = 0
-6 + -15x + -1x2 = 0 + x2 + -1x2
-6 + -15x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -15x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 15x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 15x + x2 = 0

Solving
6 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 15x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 15x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 15x + x2 = 0 + -6
15x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
15x + x2 = -6

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -6 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -6 + 56.25

Combine like terms: -6 + 56.25 = 50.25
56.25 + 15x + x2 = 50.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + 7.5) equal to 7.088723439 and -7.088723439.

Subproblem 1
x + 7.5 = 7.088723439

Simplifying
x + 7.5 = 7.088723439

Reorder the terms:
7.5 + x = 7.088723439

Solving
7.5 + x = 7.088723439

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 7.088723439 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 7.088723439 + -7.5
x = 7.088723439 + -7.5

Combine like terms: 7.088723439 + -7.5 = -0.411276561
x = -0.411276561

Simplifying
x = -0.411276561

Subproblem 2
x + 7.5 = -7.088723439

Simplifying
x + 7.5 = -7.088723439

Reorder the terms:
7.5 + x = -7.088723439

Solving
7.5 + x = -7.088723439

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -7.088723439 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -7.088723439 + -7.5
x = -7.088723439 + -7.5

Combine like terms: -7.088723439 + -7.5 = -14.588723439
x = -14.588723439

Simplifying
x = -14.588723439

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.411276561, -14.588723439}
Solution
x = {-0.411276561, -14.588723439}