x(2+6x)=300

Solution for x(2+6x)=300 equation:

Simplifying
x(2 + 6x) = 300
(2 * x + 6x * x) = 300
(2x + 6x2) = 300

Solving
2x + 6x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + 2x + 6x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-150 + x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-150 + x + 3x2)' equal to zero and attempt to solve:

Simplifying
-150 + x + 3x2 = 0

Solving
-150 + x + 3x2 = 0

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

Divide each side by '3'.
-50 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 0.3333333333x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 0.3333333333x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 0.3333333333x + x2 = 0 + 50
0.3333333333x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
0.3333333333x + x2 = 50

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = 50 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 50 + 0.25

Combine like terms: 50 + 0.25 = 50.25
0.25 + 0.3333333333x + x2 = 50.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.088723439 and -7.088723439.

Subproblem 1
x + 0.5 = 7.088723439

Simplifying
x + 0.5 = 7.088723439

Reorder the terms:
0.5 + x = 7.088723439

Solving
0.5 + x = 7.088723439

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 7.088723439 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 7.088723439 + -0.5
x = 7.088723439 + -0.5

Combine like terms: 7.088723439 + -0.5 = 6.588723439
x = 6.588723439

Simplifying
x = 6.588723439

Subproblem 2
x + 0.5 = -7.088723439

Simplifying
x + 0.5 = -7.088723439

Reorder the terms:
0.5 + x = -7.088723439

Solving
0.5 + x = -7.088723439

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -7.088723439 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -7.088723439 + -0.5
x = -7.088723439 + -0.5

Combine like terms: -7.088723439 + -0.5 = -7.588723439
x = -7.588723439

Simplifying
x = -7.588723439

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.588723439, -7.588723439}
Solution
x = {6.588723439, -7.588723439}